If the line x = 1/2, is the directrix of a parabola y^{2} – kx + 6 = 0, then which of the following is a value of ‘k’?
A.
– 4
B.
– 6
C.
– 1/4
D.
– 8
2.
Equations x = t^{2}+t+1 and y = t^{2} – t +1, represents which of the following curve?
A.
An ellipse
B.
A pair of straight
C.
A hyperbola
D.
A parabola
3.
Angle between tangents drawn from the point (2, 1) to the parabola y^{2} = – 32x is:
A.
B.
C.
D.
4.
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:
A.
(2, 0)
B.
(0, 2)
C.
(1, 0)
D.
(0, 1)
5.
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.
A.
B.
C.
D.
6.
The number of values of c such that the straight line y = 4x + c touches the curve ;is:
A.
4
B.
0
C.
Infinite
D.
2
7.
Tangents are drawn to the ellipse at the end of the latus retum. The area of the quadrilateral so formed is:
A.
54
B.
27
C.
27/2
D.
36
8.
If x = 9 is the chord of the contact of the hyperbola x^{2} – y^{2} = 9, then the equation of the corresponding pair of tangents is
A.
B.
C.
D.
9.
2x + √6 y = 2 touches the hyperbola x^{2} – 2y^{2} = 4, then the point of contact is:
A.
B.
C.
Both a & b
D.
None of these
10.
The eccentricity of hyperbola 3x^{2} – y^{2} = 4 is:
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Sample Question
Which formula is used to determine the efficiecy of the boiler based on heat absorption?