If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + …

Question

If the common tangent to the parabolas,
y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2,
 then c is equal to :

Accepted Answer

$$y = mx + {1 \over m}$$ (tangent at y2
 = 4x)

y = mx -- m2
 (tangent at x2
 = 4y)

$${1 \over m} =  - {m^2}$$ (for common tangent)

m3
 = -- 1

$$ \Rightarrow $$ m = - 1

$$ \therefore $$ Equation of tangent

y = --x --1

x + y + 1 = 0

This line touches circle whose center at (0, 0),

$$ \therefore $$ apply p( Distance from center of the circle of the line ) = r ( Radius of the circle )

c = $$\left| {{{0 + 0 + 1} \over {\sqrt 2 }}} \right| = {1 \over {\sqrt 2 }}$$

Solutions · 1