Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the po

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

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

311 Views

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


Advertisement

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


B.

45√5



Clearly, PQ is a chord of contact,
i.e., the equation of PQ is T = 0
=> y = –12

Solving with curve, 4x2 - y2 = 36



Advertisement
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


Advertisement
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


Advertisement
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


Advertisement