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

Correct option is C (34,74)
Step 1: Solve the two equations
Given equation of parabola is y^2=4x and circle x^2+y^2=5
Then x^2+4x-5=0 ⇒x^2+5x-x-5=0 ⇒x(x+5)-1(x+5)=0 ⇒(x-1)(x+5)=0 ⇒x=1,-5
At first quadrant, x=1 gives y=2
Hence, required point is A(1,2)
Step 2: Use point form of tangent equation to parabola
The equation of tangent to the parabola y^2=4ax at point (x1,y1) is yy1=2a(x+x1)
Then equation of tangent to given parabola y^2=4x at point (1,2) is
2y=2(x+1) ⇒y=x+1
Point (34,74) lies at this line
Hence, Option 'C' is correct