Q. The focal distance of a point on the parabola $y^{2} + 16x$ whose ordinate is twice the abscissa, is

A) 6
B) 8
C) 10
D) 12
Explanation

(b)
Given curve is $y^{2} = 16x$ Let any point be $(h,k)\$But$\ \ 2h = k$, then $k^{2} = 16h\$
$\ \Rightarrow \ 4h^{2} = 16h$
$\Rightarrow \ h = 0,\ h = 4\$
$\Rightarrow \ k = 0,\ k = 8\$
$\therefore$ Points are$(0,\ 0)\ ,\ (4,\ 8)$
Hence, focal distance are respectively
$0 + 4 = 4,\ 4 + 4 = 8\ \ \lbrack\because focal\ distance = h + a\rbrack$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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