Question

Co-ordinate of the focus of the parabola
$x^2-4x-8y-4=0$ are

• A. $(-3,\frac{-71}{10})$
• B. $(2,-1)$
• C. $(0,2)$
• D. $(2,1)$

Answer 1

The correct option is D $(2,1)$

Given, parabola:
$x^2-4x-8y-4=0$
$\Rightarrow (x-2{)}^2=8y+4+4$
$\Rightarrow (x-2{)}^2=8y+8$
$\Rightarrow (x-2{)}^2=8(y+1)\Rightarrow (x-2{)}^2=4\times 2(y+1)$
General equation of parabola,
$\Rightarrow (x-h{)}^2=4a(y-k)$
On comparing, we get
$h=2,a=2,k=-1$
Cooridnates of focus is $(h,k+a)$
$\Rightarrow (2,-1+2)\equiv (2,1)$
Hence, the correct answer is Option b.