Question

If the line x−1=0 is the directrix of the parabola y2−kx+8=0 , then one of the values of k is (a) 1/8 (b) 8 (c) 4 (d) 1/4

Answer 1

Answer:

Given equation of parabola is

y

2

−kx+8=0

⇒y

2

=k(x−

k

8

)

⇒(y−0)

2

=k(x−

k

8

)

The equation of the directrix of this parabola is

x−

k

8

=−

4

k

[∵x=−a]

⇒x=

k

8

−

4

k

But the equation of the directrix is given as x−1=0

∴

k

8

−

4

k

=1

⇒k

2

+4k−32=0

⇒(k−4)(k+8)=0

∴k=−8,4