Question

The focus of the parabola $y^2 - 4y - x+3=0$ is

• A. $\left( \frac{3}{4} , 2 \right)$
• B. $\left( \frac{3}{4} , - 2 \right)$
• C. $\left( 2 , \frac{3}{4} \right)$
• D. $\left( \frac{-3}{4} , 2 \right)$

Answer 1

Answer: (D)

$\left( \frac{-3}{4} , 2 \right)$

Answer 2

$y^{2}-4 y-x+3=0$ $(y-2)^{2}-4-x+3 =0$ $(y-2)^{2}-x-1 =0$ $(y-2)^{2} =(x+1)$ Let $Y^{2}=X$ ...(i) Here, $Y=(y-2), X=(x+1)$ Vertices $(X=0, Y=0)=(2,-1)$ E (i) comparing on $y^{2}=4 a x$ $4 a=1$ $\Rightarrow \, a=\frac{1}{4}$ $\therefore$ Focus $=\left(\frac{1}{4}-1,2\right)=\left(-\frac{3}{4}, 2\right)$