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

Answer: (D)

Given, equation of parabola is $y^2=4x$.
Here, $a=1$
Now, equation of tangent to the parabola in slope form is
$y=mx+\frac{a}{m}$
$\Rightarrow y=mx+\frac{1}{m}...(i)$
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 Eq.(i)]
$\Rightarrow x-y+1=0$