Parabola 1 Question 10
10. If the line $x-1=0$ is the directrix of the parabola $y^{2}-k x+8=0$, then one of the values of $k$ is
(a) $\frac{1}{8}$
(b) 8
(c) 4
(d) $\frac{1}{4}$
(2000, 2M)
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Answer:
Correct Answer: 10. (c)
Solution:
- Given,
$$ y^{2}=k x-8 $$
$$ \Rightarrow \quad y^{2}=k \quad x-\frac{8}{k} $$
Shifting the origin $Y^{2}=k X$, where $Y=y, X=x-8 / k$.
Directrix of standard parabola is $X=-\frac{k}{4}$ Directrix of original parabola is $x=\frac{8}{k}-\frac{k}{4}$
Now, $x=1$ also coincides with $x=\frac{8}{k}-\frac{k}{4}$
On solving, we get $k=4$
