Question

If the line x-1=0 is the directrix of the parabola y2 - kx + 8 = 0, k = 0 and the parabola intersects the circle x2 + y2 = 4 in two real distinct points, then the value of k is (A) -2 (B) -8 (C) 3 (D) 4​

Answer 1

Answer:

Correct option is

C

4

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

Answer 2

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