Question

Focus of the parabola $4x^2-12x+8y+13=0$ is

Answer 1

Parabola-

$4x^2-12x+3y+13=0$

$4x^2-12x+9+8y+4=0$

$3y+4=-(4x^2-12x+9)$

$8(y+\frac{1}{2})=-4(x-\frac{3}{2})$

${(x-\frac{3}{2})}^2=-2(y+\frac{1}{2})$

Compare with $x^2=4ay$

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

Now focus is at $(\frac{3}{2}a-\frac{1}{2})=(\frac{3}{2},-1)$