The tangent to the parabola y2=4x at the point where it intersects the circlex2+y2=5 in the first quadrant, passes through the point

The given equation of parabola is $y^{2} = 4 x$ …(i)

and circle is $x^{2} + y^{2} = 5$ …(ii)

From (i) and (ii), $x^{2} + 4 x - 5 = 0$

$\Rightarrow (x + 5) (x - 1) = 0 \Rightarrow x = 1$ or -5

$\Rightarrow x = 1$ and $y = 2$ [ $∵$ x and y in $1^{s t}$ quadrant]

$∵$ Equation of tangent at (1, 2) to the parabola $y^{2} = 4 x$ is $y (2) = 2 (x + 1) \Rightarrow y = x + 1$

From the options, we see that point $(3 / 4, 7 / 4)$ given in option (2) satisfy the equation of tangent.

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