The tangent to the parabola y2 = 4x at the point where it intersects the circle x2 + y2 = …

Question

The tangent to the parabola y2
 = 4x at the point
where it intersects the circle x2
 + y2
 = 5 in the
first quadrant, passes through the point :

Accepted Answer

Parabola y2
 = 4x and circle x2
 + y2
 = 5 intersect with each other.

So, x2 + 4x = 5

$$ \Rightarrow $$ x2 + 5x -- x -- 5 = 0

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

x = 1, --5

Intersection point in 1st quadrant is = (1, 2)

Equation of tangent to y2 = 4x at (1, 2) is

y(2) = 2 (x + 1)

$$ \Rightarrow $$ y = x + 1 .....(1)

By checking each options, you can see

point $$\left( { {3 \over 4},{7 \over 4}} \right)$$ lies on equation (1).

Solutions · 1