Question

The end points of the latus rectum of a parabola having vertex at origin are $(4,8)$ and $(4,-8)$ then the equation of the parabola is

• A. $y^2=4x$
• B. $y^2=8x$
• C. $y^2=16x$
• D. $x^2=8y$

Answer 1

The correct option is C $y^2=16x$

$(4,8)$ and $(4,-8)$ are ends of latus rectum
$\therefore$ midpoint is $(4,0)$
So, the focus will be $(4,0)$
Since, the vertex is $(0,0)$
$\therefore$ Parabola will be $y^2=4ax$
where $a=4$
Equation of parabola will be $y^2=16x$