Question

Find the equation of a parabola
i. having its vertex at 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

(i) $a=2$ [Ref. image]

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

(iii) $f:(0,-3)a=3y=3$

$x^2=12\left(y\right)$

$x^2=12y$

(ii) $y^2=4a(x-t)$

it will focus through $(2,2)4a=2$

$4=4+2(2-t)$

$\frac{1}{2}=2-t$

$t=2-\frac{1}{2}=\frac{3}{2}$

$t=\frac{3}{2}$

$y^2=8(x-\frac{3}{2})$