Question

The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is

• A. x + y - 4 = 0
• B. x - y + 4 = 0
• C. x - y - 1 = 0
• D. x - y + 1 = 0

Answer 1

The Correct Option is D

Given, equation of parabola is $y^{2}=4 x$. Here, $a=1$ Now, equation of tangent to the parabola in slope form is $y=m x+\frac{a}{m} $ $ \Rightarrow y=m x+\frac{1}{m}\,\,\,\,\,\,\,...(i)$ Also given that tangent to the parabola inclined at an angle of $\frac{\pi}{4}$ to the (+ve) direction of $x$ -axis. $\therefore m=\tan \frac{\pi}{4}=1 $ Then, $y=(1) x+1 \,\,\,\,\,\,$ [from E(i)] $\Rightarrow x-y+1=0$