Q. The focus of the parabola $y^{2} - x - 2y + 2 = 0\$is
A) $\left( \frac{1}{4},0 \right)$
B) (1, 2)
C) $\left( \frac{5}{4},1 \right)$
D) $\left( \frac{3}{4},\frac{5}{2} \right)$
Explanation
(c)
Given, $(y - 1)^{2} = x = 1$
$\Rightarrow Y^{2} = X,\$where$\ Y = y - 1,\ X = x - 1$
Here, $a = \frac{1}{4}$
$\therefore$ Focus is$\ (a,0)ie,\left( \frac{1}{4},0\ \right)$
$\Rightarrow \ X = \frac{1}{4},\ Y = 0$
$\Rightarrow \ x - 1 = \frac{1}{4},\ y - 1 = 0 \Rightarrow \ \ x = \frac{5}{4},\ y = 1\$
$\therefore$ Required focus is$\ \left( \frac{5}{4},1 \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.