Class XI Maths Conic Section 7

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Question 1

If the tangent at a point on the ellipse meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is:

• A
• B
• C
• D9

Question 2

A stair-case of length l rests against a vertical wall and a floor of a room,. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the stair-case begins to slide on the floor, then the locus of P is :

• Aan ellipse of eccentricity
• Ban ellipse of eccentricity
• Ca circle of radius
• Da circle of radius

Question 3

The minimum area of a triangle formed by any tangent to the ellipse and the co-ordinate axes is:

• A12
• B18
• C26
• D36

Question 4

An ellipse passes through the foci of the hyperbola, and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is, then which of the following points does not lie on the ellipse?

• A
• B
• C
• D

Question 5

If OB is the semi-minor axis of an ellipse, and are its foci and the angle between F₁B  and F₂B  is a right angle, then the square of the eccentricity of the ellipse is :

• A
• B
• C
• D

Question 6

Let PQ be a double ordinate of the parabola, y²=-4x, where P lies in the second quadrant. If R divides PQ in the ratio 2:1, then the locus of R is:

• A
• B9y²=-4x
• C3y²=2x
• D3y²=-2x

Question 7

If the tangent to the conic, at (2, 10) touches the circle, (for some fixed k) at a point; then is:

• A
• B
• C
• D

Question 8

Two tangents are drawn from a point (‒2, ‒1) to the curve, y² = 4x. If α is the angle between them, then  |tan α| is equal to

• A
• B
• C
• D3

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