Q107 / 180 · KCET 2013 · Mathematics
The equation of the tangent to the parabola $y^{2}=4 x$ inclined at an angle of $\frac{\pi}{4}$ to the positive direction of $x$-axis, is
- A$x+y-4=0$
- B$x-y+4=0$
- C$x-y-1=0$
- Correct answerD$x-y+1=0$
Solution
Given, equation of parabola is $y^{2}=4 x$.
Here, $\quad a=1$
Now, equation of tangent to the parabola in slope form is
$\begin{aligned}
y &=m x+\frac{a}{m} \\
\Rightarrow \quad y &=m x+\frac{1}{m}...(i)
\end{aligned}$
Also given that tangent to the parabola inclined at an angle of $\frac{\pi}{4}$ to the $(+\mathrm{ve})$ direction of $x$-axis.
$\begin{array}{lll}
\therefore & m=\tan \frac{\pi}{4}=1 & \\
\text { Then, } & y=(1) x+1 \\
\Rightarrow & x-y+1=0
\end{array} \quad \text { [from Eq. (i)] }$
Hence, the correct answer is option: 'D'.