JEE Questions for Maths Conic Section Quiz 2

The equation of the parabola with vertex at the origin and directrix y = 2 is

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y2 = 8x
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y2 = - 8x
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y2 = √8x
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x2 = - 8y

The length intercepted by the curve y² = 4x on the line satisfying dy/dx = 1 and passing through point (0,is given by

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1
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2
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0
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None of these

The parabola with directrix x + 2y - 1 = 0 and focus (1,is

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4x2 - 4xy + y2 - 8x + 4y + 4 = 0
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4x2 + 4xy + y2 - 8x + 4y + 4 = 0
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4x2 + 5xy + y2 + 8x - 4y + 4 = 0
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4x2 - 4xy + y2 - 8x - 4y + 4 = 0

If a point p moves such that is distances from the point A(1,and the line x + y + 2 = 0 are equal, then the locus of P is

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a straight line
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a pair of straight lines
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a parabola
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an ellipse

If the foci of an ellipse are (± √5,and its eccentricity is √5/3, then the equation of the ellipse is

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9x2 + 4y2 = 36
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4x2 + 9y2 = 36
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36x2 + 9y2 = 4
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9x2 + 36y2 = 4

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a2 + b2
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(a + b)2/ 2
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ab
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(a - b)2/ 2

If tangents are drawn to the ellipse x² + 2y² = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

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2)
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The point on the parabola y² = 64x which is nearest to the line 4x + 3y + 35 = 0 has coordinates

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(9, -24)
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(1, 81)
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(4, - 16)
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(-9, -24)

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2)
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0%

If the line x + y - 1 = 0 is a tangent to the parabola y² - y + x = 0, then the point of contact is

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(0, 1)
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(1, 0)
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(0, -1)
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(-1, 0)

If the line x cos α + y sin α = p be normal to the ellipse
Maths-Conic Section-17096.png

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p2 (a2 cos2 α + b2 sin2 α) = a2 - b2
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p2 (a2 cos2 α + b2 sin2 α) = (a2 - b2)2
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p2 (a2 sec2 α + b2 cosec2 α) = a2 - b2
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p2 (a2 sec2 α + b2 cosec2 α) = (a2 - b2)2

The line 3x + 5y = 15√2 is a tangent to the ellipse
Maths-Conic Section-17097.png

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π/6
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π/4
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π/3
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2π/3

The value of c, for which the line y = 2x + c, is tangent to the parabola y² = 4a(x + a) is

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a
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3a/2
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2a
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5a/2

The tangent to the parabola y² = 16x, which is perpendicular to a line y - 3x - 1 = 0, is

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3y + x + 36 = 0
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3y - x - 36 = 0
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x + y - 36 = 0
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x - y + 36 = 0

Three normals are drawn to the parabola y² = x passes through point (a, 0). Then

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a = 1/2
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a = 1/4
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a > 1/2
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a < 1/2

A common tangent to 9x² - 16y² = 144 and x² + y² = 9 is

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2)
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None of these

The equation of the tangents to the ellipse 4x² + 3y² = 5, which are parallel to the line y = 3x + 7, are

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2)
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None of these

The equation of normal at the point (0,of the ellipse 9x² + 5y² = 45, is

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X - axis
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Y - axis
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y + 3 = 0
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y - 3 = 0

If the line lx + my = 1 is a normal to the hyperbola
Maths-Conic Section-17104.png

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a2 - b2
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a2 + b2
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(a2 + b2)2
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(a2 - b2)2

A line touches the circle x² + y² = 2 and the parabola y² = 8x, then equation of tangent is

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y = x + 3
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y = x + 2
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y = x + 4
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y = x + 1

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2)
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None of these

The equation of the normal at a point (a sec θ, b tan θ) of the curve b²x² - a²y² = a² b², is

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2)
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0%

The equation of the chord of the circle x² + y² - 4x = 0, whose mid - point is (1,is

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y = 2
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y = 1
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x = 2
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x = 1

The middle point of the chord x + 3y = 2 of the conic x² + xy - y² = 1, is

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(5, -1)
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(1, 1)
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(2, 0)
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(-1, 1)

The mid - point of the chord 4 x - 3y = 5 of the hyperbola 2 x² - 3y² = 12, is

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(2, 1)
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0%

The length of the common chord of the parabolas y² = x and x² = y, is

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2√2
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1
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√2
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1/√2

The locus of middle points of chords of hyperbola
3x² - 2y² + 4x - 6y = 0 parallel to y = 2x, is

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3x - 4y = 4
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3y - 4x + 4 = 0
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4x - 3y = 3
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3x - 4y = 2

If a focal chord of parabola y² = 16x cuts it at points (f, g) and (h, k). Then f, h is equal to

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12
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16
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14
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None of these

If the parabola y² = 4ax, the length of the chord passing through the vertex inclined to the axis at π/4, is

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4a√2
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2a√2
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a√2
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a

If the chords of contact of tangents from two points (x₁, y₁) and (x₂, y₂) to the hyperbola 4x² - 9y² - 36 = 0 are right angles, then
Maths-Conic Section-17118.png

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9/4
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- (9/4)
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81/16
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- (81/

If a focal chord of the parabola y² = ax is 2x - y - 8 = 0, then the equation of the directrix is

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x + 4 = 0
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x - 4 = 0
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y - 4 = 0
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y + 4 = 0

The length of the chord of the parabola y² = 4ax, which passes through the vertex and makes an angle α with the axis of the parabola is

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4a cos α cosec2 α
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4a α cosec2 α
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a cos α cosec2 α
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a cos α cosec α

The equation of hyperbola whose asymptotes are 3x ± 5y = 0 and vertices are (± 5,is

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3x2 - 5y2 = 25
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5x2 - 3y2 = 225
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25x2 - 9y2 = 225
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9x2 - 25y2 = 225

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x2 + y2 = 16
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x2 + y2 = 25
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x2 + y2 = 9
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x2 + y2 = 41

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2)
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If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

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2)
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1/√2
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√3/2
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1√3
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1/2

The value of k, if (1, 2), (k -are conjugate points with respect to the ellipse 2x² + 3y² = 6, is

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2
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4
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6
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8

Equation of asymptotes of xy = 7x + 5y are

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x = 7, y = 5
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x = 5, y = 7
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xy = 35
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None of these

For the parabola y² + 8x -12y +20=0

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vertex is (2, 6)
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focus is (0, 6)
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latusrectum 4
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axis Y = 6

The equation of the hyperbola having its eccentricity 2 and the distance between its focii is 8, is

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2)
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A point P on an ellipse is at a distance 6 units from a focus. lithe eccentricity of the ellipse is 3/5, then the distance of P from the corresponding directrix is