Question

Find the equation of a parabola
(i) having its vertex ar A (1,0) and focus at S(3, 0)
(ii) having its focus at S(2, 0) and one extremity of its latus rectum at (2, 2)
(iii) having focus at (0, -3) and directrix y=3

Answer 1

$1)$The equation of parabola with vertex $(h,k)$ is $(y-k{)}^2=4a(x-h)$

$⟹(y-0{)}^2=4a(x-1)$

$a=3-1=2$

$y^2=8(x-1)$

$2)a=\sqrt{(2-2{)}^2+(2-0{)}^2}=2$

$(h,k)=(2-2,0)=(0,0)$

$y^2=8x$

$3)a=3⟹y^2=-12x$