Question

The ends of the latus rectum of the parabola $x^2+10x-16y+25=0$ are

• A. (3, 4), (-13, 4)
• B. (5, -8), (-5, 8)
• C. (3, -4), (13, 4)
• D. (-3, -4), (13, -4)

Answer 1

Answer: (A)

We have, $x^2+10x-16y+25=0$
$\Rightarrow {\left(x+5\right)}^2=16y$ ...(i)
$\Rightarrow X^2=4\times 4y$
Ends of latus rectum of a parabola is $(\pm 2a,a)$
$\Rightarrow X=2a,X=-2a\Rightarrow x+5=8,x+5=-8$
$\Rightarrow x=3,x=-13$
From (i) when $x=3,y=4$; when $x=-13,y=4$
$\therefore$ Required points are (3, 4), (-13, 4)