Question

The equation of the normal to the curve $x^2=4y$ at (1, 2) is

• A. 2x + y + 4 = 0
• B. 2x + y – 4 = 0
• C. 2x – y + 4 = 0
• D. 2x – y – 4 = 0

Answer 1

The correct option is B 2x + y – 4 = 0

$x^2=4y\Rightarrow 2x=4\frac{dy}{dx}\Rightarrow \frac{dy}{dx}=\frac{x}{2}\Rightarrow {\left[\frac{dy}{dx}\right]}_{(1,2)}=\frac{1}{2^{.}}$
$\therefore$ Slope of the normal = –2
Equation of the normal is $y–2=–2(x–1)\Rightarrow y–2=–2x+2\Rightarrow 2x+y–4=0$