Question

For the parabola $y^2 = 4x$, the point $P$ whose focal distance is $17$, is

• A. (16, 8) or (16,-8)
• B. (8, 8) or (8,-8)
• C. (4, 8) or (4,-8)
• D. (2, 8) or (2,-8)

Answer 1

Answer: (A)

Given, $y^{2}=4 x$
Let $P(h, k)$ be any point on the parabola
$\therefore \,\,\,\,\,\,\,(h-1)^{2}+(k-0)^{2}=17^{2}$
Also, $k^{2}=4 h$
$\therefore \,\,\,\,\,\,\,h^{2}+1-2 h+4 h=289$
$\Rightarrow \,\,\,\,\,\,\, h^{2}+2 h-288=0$
$\Rightarrow \,\,\,\,\,\,\,(h+18)(h-16)=0$
$\Rightarrow \,\,\,\,\,\,\, h=16 \,\,\,\,\,\,\,(\because h$ cannot be negative)
$\therefore \,\,\,\,\,\,\, k^{2}=64$
$\Rightarrow \,\,\,\,\,\,\, k=\pm 8$
$\therefore $ Points are $(16,8)$ or $(16,-8)$