Question

Equation of the parabola whose vertex is $(-3,-2)$, axis is horizontal and which passes through the point $(1,2)$ is

• A. $y^2+4y+4x-8=0$
• B. $y^2+4y-4x+8=0$
• C. $y^2+4y-4x-8=0$
• D. none of these

Answer 1

The correct option is C $y^2+4y-4x-8=0$

Since the axis is horizontal and vertex is $(-3,-2)$ and passes through $(1,2)$.
$\therefore$ the equation of the parabola must be of the form
$(y+2{)}^2=4a(x+3)$
It passes through $(1,2)$,
$\therefore 16=16a\Rightarrow a=1$

Hence, the equation of the required parabola is
$(y+2{)}^2=4(x+3)$
or $y^2+4y-4x-8=0$