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 Multiple Choice QuestionsMultiple Choice Questions

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41.

The eccentricity of an ellipse, with its centre at the origin, is 1 /2 . If one of the directrices is x = 4, then the equation of the ellipse is

  • 3x2 +4y2 = 1

  • 3x2+ 4y2 = 12

  • 4x2 +3y2 = 12

  • 4x2 +3y2 = 12


B.

3x2+ 4y2 = 12

Since the directrix is x = 4 then ellipse is parallel to X-axis.
⇒ a/e = 4
⇒ a = 4e = 4 x (1/2)
⇒ a = 2
Also we know that
b2 =a2 (1-e2)
b2 = 4(1-1/4) = 4 x 3/4
b2 = 3
therefore equation of ellipse is
straight x squared over 4 space plus straight y squared over 3 space equals space 1
3 straight x squared space plus space 4 straight y squared space equals space 12

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42.

PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45o, 30o and 30o, then the height of the tower (in m) is

  • 50√2

  • 100

  • 50

  • 100√3


43.

Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of △PTQ is

  • 36√5

  • 45√5

  • 54√3

  • 60√3


44.

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the
parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and,∠CPB = θ then a value of tan θ is

  • 4/3

  • 1/2

  • 2

  • 3


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45.

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

  • 3x + 2y = 6xy

  • 3x + 2y = 6

  • 2x + 3y = xy

  • 3x + 2y = xy


46.

Let P be the foot of the perpendicular from focus S of hyperbola x2a2 - y2b2 = 1 on the line bx- ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is

  • 2ab

  • ab

  • a2 + b22

  • ab


47.

B is an extremity of the minor axis of an ellipse whose foci are S and S'. If SBS' is a right angle, then the eccentricity of the ellipse is

  • 12

  • 12

  • 23

  • 13


48.

The axis of the parabola x2 + 2xy + y- 5x + 5y - 5 = 0 is

  • x + y = 0

  • x + y - 1 = 0

  • x - y + 1 = 0

  • x - y = 12


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49.

The line segment joining the foci of the hyperbola x2 - y2 + 1 = 0 is one of the diameters of a circle. The equation of the circle is

  • x+ y2 = 4

  • x+ y22

  • x+ y2 = 2

  • x+ y222


50.

If one of the diameters of the curve x2 + y2 - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is

  • 3

  • 2

  • 2

  • 1


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