Question

Equation of the parabola obtained by taking reflection of $y=4x^2-4x+3$ about the line $y=x,$ will be

• A. ${(y-\frac{1}{2})}^2=\frac{1}{4}(x-2)$
• B. ${(y-\frac{1}{2})}^2=4(x-2)$
• C. ${(y-2)}^2=\frac{1}{4}(x-\frac{1}{2})$
• D. ${(y-2)}^2=4(x-\frac{1}{2})$

Answer 1

The correct option is A ${(y-\frac{1}{2})}^2=\frac{1}{4}(x-2)$

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

To get the reflected equation about the line $y=x$, we have to interchange $x$ and $y.$
Hence, required equation is ${(y-\frac{1}{2})}^2=\frac{1}{4}(x-2)$