Question

Length of the latus rectum of the parabola $y=4x^2-4x+3$ will be

• A. $\frac{1}{4}$ units
• B. $2$ units
• C. $\frac{3}{2}$ units
• D. $4$ units

Answer 1

The correct option is A $\frac{1}{4}$ units

$y=4x^2-4x+3$
$\Rightarrow y=(2x-1{)}^2+2$
$\Rightarrow y-2=4{(x-\frac{1}{2})}^2$
$\Rightarrow {(x-\frac{1}{2})}^2=\frac{1}{4}(y-2)$
Comparing it with equation of parabola $X^2=4aY$
Length of latus rectum will be $=4a$
So here, length of latus rectum $=\frac{1}{4}$ units