The tangent to the parabola y^2=4x at the point where it intersects the circle x^2+y^2=5 i…

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:

Accepted Answer

Intersection: $x^2+4x-5=0\Rightarrow x=1,\ y=2$ (first quadrant).

Tangent at $(1,2)$: $2y=2(x+1)\Rightarrow y=x+1$.

Checking $\left(\frac34,\frac74\right)$: $\frac74=\frac34+1$ .

Solutions · 1