Let x2a2 + y2b2 = 1 a > b&n

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 Multiple Choice QuestionsMultiple Choice Questions

421.

Let x24 + y23 = 1 is an ellipse and a hyperbola which is confocal with ellipse such thatits transverse axis is 2 then which of following point does not lie on hyperbola

  • 1, - 12

  • -32, 1

  • 32, 12

  • None of these


 Multiple Choice QuestionsShort Answer Type

422.

The centre of circle lies on x + y = 3 and touching the lines x = 3, y = 3 then find diameter of circle


 Multiple Choice QuestionsMultiple Choice Questions

423.

Let e1 and e2 be the eccentricities of the ellipse, x225 + y2b2 = 1b < 5 and the hyperbola, x216 - y2b2 = 1respectively satisfying e1e= 1. If α and β are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair α, β is equal to:

  • (8, 10)

  • 203, 12

  • (8, 12)

  • 245, 10


 Multiple Choice QuestionsShort Answer Type

424.

If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is.....


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 Multiple Choice QuestionsMultiple Choice Questions

425.

Let P(3, 3) be a point on the hyperbola,x2a2 - y2b2 = 1 . If the normal to it at P intersects the x-axis at (9,0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :

  • 92, 3

  • 32, 2

  • 9, 3

  • 92, 2


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426.

Let x2a2 + y2b2 = 1 a > b be agiven ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function φt = 512 + t - t2 then a+ b2 is equal to

  • 145

  • 126

  • 116

  • 135


B.

126

LR = 2b2a = 10  b2 = 5aφt = 512 - t2 - t + 14 - 14= 512 + 14 - t - 122= 23 - t - 122max φt = 23 = eb2 = a21 - e25a = a21 - 49 5 = 59a a2 = 81, b2 = 45a2 + b2 = 126


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427.

The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x+ y2 – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the point :

  • 1, - 3

  • - 1, 3

  • ( - 3, 6)

  • ( - 3, 1)


428.

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 21. If P(1, β), β > 0 is a point on this ellipse, then the equation of the normal to it at P is

  • 7x - 4y = 1

  • 4x - 2y = 1

  • 8x - 2y = 5

  • 4x - 3y = 2


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 Multiple Choice QuestionsShort Answer Type

429.

Let PQ be a diameter of the circle x2 + y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line,  x + y = 2 respectively, then the maximum value of αβ is .....


 Multiple Choice QuestionsMultiple Choice Questions

430.

If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2, then c is equal to :

  • 12

  • 122

  • 12

  • 14


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