If e and e' are the eccentricities of the ellipse 5x2 + 9y2&

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 Multiple Choice QuestionsMultiple Choice Questions

271.

The products of lengths of perpendiculars from any point of hyperbola x2 - y2 = 8 to its asymptotes, is

  • 2

  • 3

  • 4

  • 8


272.

The equation 16x2 + y2 + 8xy - 74x - 78y + 212 = 0 represents

  • a circle

  • a parabola

  • an ellipse

  • a hyperbola


273.

Equation of curve in polar coordinates is lr = 2sin2θ2 represents

  • a straight line

  • a parabola

  • a circle

  • an ellipse


274.

iF a is a complex number and b is a real number, then the equation a + a + b = 0 represents a

  • straight line

  • parabola

  • circle

  • hyperbola


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275.

The equation of the circle of radius 5 and touching the co-ordinate axes in third quadrant is

  • (x - 5)2+ (y + 5)2 = 25 

  • (x + 5)2 + (y + 5)2 = 25

  • (x + 4)2 + (y + 4)2 = 25

  • (x + 6)+ (y + 6)= 25


276.

The four distinct points (0, 0), (2, 0), (0, - 2)and (k, - 2) are concyclic, if k is equal to

  • 3

  • 1

  • - 2

  • 2


277.

A line is at a constant distance c from the origin and meets the coordinate axes in A and B. The locus of the centre of the circle passing through O, A, B is

  • x2 + y2 = c2

  • x2 + y2 = 2c2

  • x2 + y2 = 3c2

  • x2 + y2 = 4c2


278.

The line y = mx + c intercepts the circle x2 + y2 = r2 in two distinct points, if

  • - r1 + m2 < c < r1 + m2 

  •  c < - r1 + m2 

  •  c < r1 + m2 

  • None of the above


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279.

The equation of the parabola with the focus (3, 0) and the directrix x + 3 = 0, is

  • y2 = 3x

  • y2 = 6x

  • y2 = 12x

  • y2 = 2x


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280.

If e and e' are the eccentricities of the ellipse 5x2 + 9y2 = 45 and the hyperbola 5 - 4y = 45 respectively, then ee' is equal to

  • 1

  • 4

  • 5

  • 9


A.

1

Equation of the ellipse is

5x2 + 9y2 = 45

or           x29 + y25 = 1    ...i

   e = 1 - b2a2 =1 - 59 = 23and equation of hyperbola is            5x2 - 4y2 = 45or   x29 - y2454 = 1     ...iie' = 1 + b2a2 = 1 + 4536 = 8136 = 96 = 32Thus            ee' = 23 32 = 1

 


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