JEE Questions for Maths Conic Section Quiz 10

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The line x + y = 6 is normal to the parabola y² = 8x at the point

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(4, 2)
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(2, 4)
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(2, 2)
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(3, 3)

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–4
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4
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0
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6

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If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is

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If distance between the directrices be thrice the distance between foci, then eccentricity of ellipse is

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The equation of the ellipse whose centre is at origin and which passes through the points (–3,and (2, –2)

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If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is

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12
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15
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If the foci and vertices of an ellipse be (±1,and (±2, 0), then the minor axis of the ellipse is

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2
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4
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The equations of the directrices of the ellipse 16x² + 25y² = 400 are

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2x = ± 25
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5x = ±9
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3x = ± 10
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None of these

The eccentricity of an ellipse is 2/3, latus rectum is 5 and centre is (0, 0). The equation of the ellipse is

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The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is

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None of these

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8
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12
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18
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24

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2
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4
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6
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8

The equation of the ellipse whose vertices are (±5,and foci are (±4,is

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None of these

The equation of the ellipse whose foci are (±5,and one of its directrix is 5x = 36 is

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None of these

If the eccentricity of an ellipse be 1/√2, then the latus rectum is equal to its

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Minor axis
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Semi-minor axis
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Major axis
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Semi-major axis

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If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is

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For each point (x, y) on an ellipse the num of the distances from (x, y) to the points (2,and (–2,is 8. Then the positive value of x so that (x,lies on the ellipse is

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2
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4
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0

The length of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along the y-axis. The equation of the ellipse referred to its centre as origin is

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If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0,and 5 then its equation is

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None of these

The equation of the ellipse whose one of the vertices is (0,and the corresponding directrix is y = 12 is

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None of these

The equation 2x² + 3y² = 30 represents

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A circle
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An ellipse
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A hyperbola
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A parabola

The equation of the ellipse whose latus rectum is 8 and whose eccentricity is 1/√2, referred to the principal axis of coordinates is

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Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points is

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The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

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A point ratio of whose distance from a fixed point and line x = 9/2 is always 2 : 3. Then locus of the point will be

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Hyperbola
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Ellipse
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Parabola
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Circle

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An ellipse
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A hyperbola
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A parabola
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A circle

The length of the latus rectum of an ellipse is 1/3 of the major axis. Its eccentricity is

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An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cm are

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None of these

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r > 2
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2 < r < 5
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r > 5
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None of these

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The equation of the ellipse whose one focus is at (4,and whose eccentricity is 4/5 is

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(±3, 0)
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(0, ±3)
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(3, –3)
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(–3, 3)

The focus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant k (

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Circle
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Hyperbola
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Ellipse
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Straight line

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x² + 9y² = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is

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The normal at a point P on the ellipse x² + 4y² = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectum of the given ellipse at the points