If the normal at an end of latus rectum of an ellipse passes thro

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 Multiple Choice QuestionsMultiple Choice Questions

431.

If the co–ordinates of two points A and B are 7, 0 and  - 7, 0 respectively and P is any point on the conic, 9x2 + 16y2 = 144, then PA + PB is equal to :

  • 8

  • 16

  • 9

  • 6


432.

If the line y = mx + c is a common tangent to the hyperbola x2100 - y264 = 1 and the circle x2 + y2 = 36, then which one of the following is true 

  • 4c2 = 369

  • 5m = 4

  • c2 = 369

  • 8m + 5 = 0


433.

If the length of the chord of the circle, x2 + y2 = r2(r > 0) along the line, y – 2x = 3 is r, then r2 is equal to :

  • 95

  • 12

  • 125

  • 245


434.

Let L1 be a tangent to the parabola y2 = 4(x + 1) and L2 be a tangent to the parabola y2 = 8(x + 2) such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line :

  • x + 3 = 0

  • 2x + 1 = 0

  • x + 2y = 0

  • x + 2 = 0


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435.

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse,  x24 + y22 = 1 from any of its foci?

  •  - 2, 3

  •  - 1, 2

  • (1, 2)

  •  - 1, 3


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436.

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, the eccentricity e of the ellipse satisfies : 

  • e4 + 2e2 - 1 = 0

  • e2 +  e - 1

  • e2 + 2e - 1 = 0

  • e4 + e2 - 1 = 0


D.

e4 + e2 - 1 = 0

Equationof normal at ae, b2a

a2xae - b2yb2a = a2 - b2It passes through 0, - bab = a2e2a2b2 = a4e4  b2 = a21 - e21 - e2 = e4


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437.

The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is:

  • 310, 165

  • - 5310, 165

  •  - 165, 5310

  • 65, 5310


438.

The radius of the larger circle lying in the first quadrant and touching the line 4x + 3y - 12 =0 and the co-ordinate axes,is

  • 5

  • 6

  • 7

  • 8


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439.

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

  • 4x2 - 4xy + y2 - 8x + 4y + 4 = 0

  • 4x2 + 4xy + y2 - 8x + 4y + 4 = 0

  • 4x2 + 5xy + y2 + 8x - 4y + 4 = 0

  • 4x - 4xy + y - 8x - 4y + 4 = 0


440.

The length of the common chord of the circles of radii 15 and 20, whose centres are 25 unit of distance apart, is

  • 12

  • 16

  • 24

  • 25


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