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The tangent to the parabola

Question:

The tangent to the parabola $\mathrm{y}^{2}=4 \mathrm{x}$ at the point where it intersects the circle $x^{2}+y^{2}=5$ in the first quadrant, passes through the point :

  1. $\left(-\frac{1}{3}, \frac{4}{3}\right)$

  2. $\left(-\frac{1}{4}, \frac{1}{2}\right)$

  3. $\left(\frac{3}{4}, \frac{7}{4}\right)$

  4. $\left(\frac{1}{4}, \frac{3}{4}\right)$

Correct Option: , 3

Solution:

Given $\mathrm{y}^{2}=4 \mathrm{x}$ .............(1)

and $x^{2}+y^{2}=5$ ..............(2)

by $(1)$ and (2)

$\Rightarrow x=1$ and $y=2$

equation of tangent at $(1,2)$ to $\mathrm{y}^{2}=4 \mathrm{x}$ is $y=x+1$

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