Question

If the vertex of a parabola is $(0,1)$ and its directrix is $2y=5$, then its equation will be:

• A. $y^2+6x=6$
• B. $y^2+6y=6$
• C. $x^2=6y+6$
• D. $x^2+6y=1$

Answer 1

The correct option is D $x^2+6y=1$

Equation of direction $\Rightarrow y=\frac{5}{2}$

Equation of tangent of vertex $\Rightarrow y=1$

$\Rightarrow (y-1)=0$

distance between vertex & direction $=3$

$\Rightarrow 0x+2y-5=0$

$(0,1)$

$\frac{0+2-5}{2}=\frac{-3}{2}$

equation of axis $\Rightarrow x=0$

eqn of parabola $\Rightarrow x^2=4\left(\frac{-3}{2}\right)(y-1)$

$x^2=-6(y-1)$

$x^2+6y=6$