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 :
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 $y=x+1$