If the ellipse 9x2 + 16y2 = 144 intercepts the line&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

31.

What is the radius of the circle passing through thpoint (2, 4) and having centre at the intersection of the lines - = 4 and 2x + 3y + 70 = 0 ?

  • 3 units

  • 5 units

  • 33 units

  • 52


32.

What is the equation of the hyperbola having latus rectum and eccentricity 8 and 35 respectively.

  • x225 - y220 = 1

  • x240 - y220 = 1

  • x240 - y230 = 1

  • x230 - y225 = 1


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33.

If the ellipse 9x2 + 16y2 = 144 intercepts the lin3x + 412, then what is the length of the chord sforme?

  • 5 units

  • 6 units

  • 8 units

  • 10 units


A.

5 units

Here,9x2 + 16y2 = 144 and      3x + 4y = 12  x = 12 - 4y3So,912 - 4y32 + 16y2 = 144On solving we get, y = 0, 3For y = 0, x= 4For y= 3, x = 0 Length of chord  = 0 - 32 + 4 - 02 = 9 + 16 = 25 = 5 units


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34.

What is the eccentricity of rectangular hyperbola ?

  • 2

  • 3

  • 5

  • 6


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35.

What is the curve which passes through the point (1, 1and whose slope i2yx ?

  • Circle

  • Parabola

  • Ellipse

  • Hyperbola


36.

Consider the parabola y = x2 + 7x and the straight liney = 3- 3.

What are the coordinates of the point on the parabola which is closest to the straight line ?

  • (0, 2)

  • ( - 2,  - 8)

  • ( - 7, 2)

  • (1, 10)


37.

Consider the parabola y = x2 + 7x and the straight liney = 3- 3.

What is the shortest distance from the above point on the parabola to the lin?

  • 102

  • 105

  • 110

  • 54


38.

If the angle between the lines joining the end points of minor axis of the ellipse x2a2 + y2b2 = 1 with one of its foci is π2, then what is the eccentricity of the ellipse ?

  • 12

  • 12

  • 32

  • 122


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39.

In the parabola, y2 = x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle θ ?

  • sin(θ) . sec2(θ)

  • cos(θ) . cosec2(θ)

  • cot(θ) . sec2(θ)

  • 2tan(θ) . cosec2(θ)


40.

Let P(x, y) be any point on theellipse 25x2 + 16y2 = 400. If Q(0, 3) and R(0, 3) are two points, then what is (PQ + PR)

  • 12

  • 10

  • 8

  • 6


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