Question:
Find the equation of the parabola with focus $F(4,0)$ and directrix $x=-4$.
Solution:
Given equation of directrix : $x=-4$
• x + 4 = 0
Above equation is of the form, $x+a=0$
Focus of the parabola $F(4,0)$ is of the form $F(a, 0)$
Therefore, $\mathrm{a}=4$
For directrix with equation $\mathrm{x}+\mathrm{a}=0$ and focus $(\mathrm{a}, 0)$, equation of the parabola is,
$y^{2}=4 a x$
$\cdot y^{2}=16 x$
