The radius of a circle, having minimum area, which touches the curve y = 4 - x 2 and the lines, y = x is:

Question

Aicharya · Accepted Answer

Length of perpendicular from centre of circle to tangent line $r = \frac{k}{\sqrt{2}}$

And $r = |4 - k|$

$\Rightarrow r = 4 - k = \frac{k}{\sqrt{2}}$

$\Rightarrow 4 = \frac{k + \sqrt{2} k}{\sqrt{2}}$

$\Rightarrow k = \frac{4 \sqrt{2}}{\sqrt{2} + 1}$

$\Rightarrow r = \frac{4 \sqrt{2}}{(\sqrt{2} + 1) \sqrt{2}}$

$\Rightarrow r = \frac{4}{\sqrt{2} + 1}$

$\Rightarrow r = 4 (\sqrt{2} - 1)$

The radius of a circle, having minimum area, which touches the curve y = 4 - x 2 and the lines, y = x is:

Solution