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