Question

Find the equation of the parabola with vertex at the origin, axis along the X-axis and passing through the point (i) (1, -4) (ii) (2, 3).

Answer 1

The equation of parabola passing through origin and axis along $x$ axis

is given as $y^2=4ax$

$i)$ it is passing through $(1,-4)$

$(-4{)}^2=4a(1)$

$16=4a$

$a=4$

$⟹y^2=16x$

$ii)$ it is passing through $(2,3)$

$(3{)}^2=4a(3)$

$9=12a$

$a=\frac{3}{4}$

$⟹y^2=3x$