Question

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 :

• A. $(-\frac{1}{3},\frac{4}{3})$
• B. $(-\frac{1}{4},\frac{1}{2})$
• C. $(\frac{3}{4},\frac{7}{4})$
• D. $(\frac{1}{4},\frac{3}{4})$

Answer 1

The correct option is C $(\frac{3}{4},\frac{7}{4})$

$y^2=4x,x^2+y^2=5$
The point of intersection of the two curves in the first quadrant is $(1,2)$.
Equation of tangent to the parabola $y^2=4x$ at $(x_1,y_1)=(1,2)$ is $y{y}_1=4\left(\frac{x+x_1}{2}\right)$
$\Rightarrow y=x+1$
$(\frac{3}{4},\frac{7}{4})$ passes through the line $y=x+1$