JEE Main: Co-ordinate Geometry Exam Quiz!

1. 2x + √6 y = 2 touches the hyperbola x² – 2y² = 4, then the point of contact is:

Both a & b

None of these

Explanation

2. If the line x = 1/2, is the directrix of a parabola y² – kx + 6 = 0, then which of the following is a value of 'k'?

– 4

– 6

– 1/4

– 8

Explanation

3. If x = 9 is the chord of the contact of the hyperbola x² – y² = 9, then the equation of the corresponding pair of tangents is

Explanation

4. Tangents are drawn to the ellipse

x squared over 9 plus y squared over 8 equals 1

at the end of the latus retum. The area of the quadrilateral so formed is:

54

27

27/2

36

Explanation

5. A parabola has the origin at it focus and the line x = 2 as its directrix. Then the vertex of the parabola will be at:

(2, 0)

(0, 2)

(1, 0)

(0, 1)

from the diagram it is clear that the vertex will be the midpoint of OP So co-ordinate of vertex are (1, 0)

Explanation

from the diagram it is clear that the vertex will be the midpoint of OP So co-ordinate of vertex are (1, 0)

6. The eccentricity of hyperbola 3x² – y² = 4 is:

1

5

– 2

2

Explanation

7. Equations x = t²+t+1 and y = t² – t +1, represents which of the following curve?

An ellipse

A pair of straight

A hyperbola

A parabola

Explanation

8. Angle between tangents drawn from the point (2, 1) to the parabola y² = – 32x is:

Explanation

9. The eccentricity of the ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then which of the following correctly represent the equation of ellipse.

Explanation

10. The number of values of c such that the straight line y = 4x + c touches the curve

x squared over 4 plus y squared equals 1

;is:

4

0

Infinite

2

Explanation