A set of parallel chords of the parabola y 2 = 4ax have their mid-point on

Any straight line parallel to the axis

Any straight line through the vertex

Any straight line through the focus

JEE Questions for Maths Conic Section Quiz 9

The equation of the tangent to the parabola y² = 9x which goes through the point (4,is
a. x + 4y + 1 = 0
b. 9x + 4y + 4 = 0
c. x – 4y + 36 = 0
d. 9x – 4y + 4 = 0

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c and d
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only c
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only b
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only a

Two perpendicular tangents to y² = 4ax always intersect on the line is

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x = a
0%
x = a
0%
x = a
0%
x + 4a = 0

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0%
2)
0%
0%

The two tangents drawn from a point P to the parabola y² = 4x are at right angles, then the locus of P is

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x = 1
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2x + 1 = 0
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x = –1
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x = –1

The tangent drawn at any point P the parabola y² = 4ax meets the directrix at the point K, then the angle which KP subtends at its focus is

0%
30o
0%
45o
0%
60o
0%
90o

The normal meet the parabola y² = 4ax at the point where the abscissa of the point is equal to the ordinate of the point is

0%
(6a, –9a)
0%
(–9a, 6a)
0%
(–6a, 9a)
0%
(9a, –6a)

0%
0%
2)
0%
0
0%

0%
0o
0%
90o
0%
60o
0%
30o

If the tangent to the parabola y² = ax makes an angle of 45^o with x-axis, then the point of contact is

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0%
2)
0%
0%

The number of parabolas that can be drawn if two ends of the latus rectum are given

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2
0%
1
0%
4
0%
3

The point of the intersection of tangents at the ends of the latus rectum of the parabola y² = 4x is equal to

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(1, 0)
0%
(–1, 0)
0%
(0, 1)
0%
(0, –1)

The angle between the tangents drawn from the points (1,to the parabola y² = 4x is

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0%
2)
0%
0%

The locus of the middle points of the chords of the parabola y² = 4x which passes through the origin

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y2 = ax
0%
y2 = 2ax
0%
y2 = 4ax
0%
x2 = 4ay

The point on the parabola y² = 8x at which the normal is parallel to the line x – 2y + 5 = 0 is

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0%
2)
0%
0%

The maximum number of normal that can be drawn from a point to a parabola is

0%
0
0%
1
0%
2
0%
3

The point on the parabola y² = 8x at which the normal is inclined at 60^o to the x-axis has the coordinates

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0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

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

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0%
2)
0%
0%
None of these

The equation of a straight line drawn through the focus of the parabola y² = -4x at an angle of 1200 to the x-axis is

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0%
2)
0%
0%

Through the vertex of the parabola y² = 4x chords OP and OQ are drawn at right angles to one another. The locus of middle points of PQ is

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0%
2)
0%
0%

In the parabola y² = 6x, the equation of the chord through vertex and negative end of laws rectum, is

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y = 2x
0%
x = 2y
0%
y + 2x = 0
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x + 2y = 0

The length of chord of contact of the tangents drawn from the point (2,to the parabola y² = 8x, is

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0%
2)
0%
0%

If ‘a’ and ‘c’ are the segments of a focal chord of a parabola and b the semi-latus rectum, then

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a, b, c are in A.P.
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a, b, care in G.P.
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a, b, c are in H.P.
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None of these

If the segment intercepted by the parabola y² = 4ax with the line lx + my + n = 0 subtends a right angle at

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4a1 + n = 0
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4a1+4am+ n = 0
0%
4am + n = 0
0%
a1 + n = 0

A set of parallel chords of the parabola y² = 4ax have their mid-point on

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Any straight line through the vertex
0%
Any straight line through the focus
0%
Any straight line parallel to the axis
0%
Another parabola

The equations of the normals at the ends of laws rectum of the parabola y² = 4ax are given by

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x2 – y2 – 6ax + 9a2 = 0
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x2 – y2 – 6ax – 6ay + 9a2 = 0
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x2 – y2 – 6ay + 9a2= 0
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None of the above

If the normals at two points P and Q of a parabola y² = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is

0%
4a2
0%
2a2
0%
– 4a2
0%
8a2

0%
0%
2)
0%
0%

0%
6
0%
4
0%
3
0%
None of these

At what point on the parabola y² = 4x, the normal makes equal angles with the coordinate axes

0%
(4, 4)
0%
(9, 6)
0%
(4, –4)
0%
(1, –2)

Equation of any normal to the parabola y² = 4a(x – a) is

0%
0%
2)
0%
0%

Tangents drawn at the ends of any focal chord of a parabola y² = 4ax intersect in the line

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y – a = 0
0%
y + a = 0
0%
x – a = 0
0%
x + a = 0

The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola y² = 4ax, lies on

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Axis
0%
Directrix
0%
Latus rectum
0%
Tangent at vertex

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0%
2)
0%
0%

The length of the normal chord to the parabola y² = 4x, which subtend right angle at the vertex is

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0%
2)
0%
2
0%
1

If x + y = k is a normal to the parabola y² = 12x, then k is

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3
0%
9
0%
–9
0%
–3

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0%
2)
0%
0%

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0%
2)
0%
0%

From the point (–1, –two tangents are drawn to the parabola y² = 4x. Then the angle between the two tangents is

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30o
0%
45o
0%
60o
0%
90o

The polar of focus of parabola

0%
x-axis
0%
y-axis
0%
Directrix
0%
Latus rectum

Equation of diameter of parabola y² = x corresponding to the chord x – y + 1 = 0 is

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2y = 3
0%
2y = 1
0%
2y = 5
0%
y = 1

The area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus rectum is

0%
12 sq,unit
0%
16 sq. unit
0%
18 sq. unit
0%
24 sq. unit

The area of triangle formed inside the parabola y² = 4x and whose ordinates of vertices are 1, 2 and 4 will be

0%
0%
2)
0%
0%

An equilateral triangle is inscribes in the parabola y² = 4ax whose vertices are at the parabola, then the length of its side is equal to

0%
8a
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%

From the point (–1,tangent lines are drawn to the parabola y² = 4x, then the equation of chord of contact is

0%
y = x + 1
0%
y = x – 1
0%
y + x = 1
0%
None of these

For the above problem, the area of triangle formed by chord of contact and the tangent is given by

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8
0%
2)
0%
0%
None of these

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0%
2)
0%
0%

If axis of the parabola y = f(x) is parallel to y – axis and it touches the line y = x at (1, 1), then

0%
0%
2)
0%
0%

JEE Questions for Maths Conic Section Quiz 9 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Conic Section Quiz 9 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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