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Question: A circle touches both axes and line x – y = a\(\sqrt{2}\) (a \> 0) then centre of circle can be...

A circle touches both axes and line x – y = a2\sqrt{2} (a > 0) then centre of circle can be

A

(a, a)

B

(a, –a)

C

(–a, a)

D

None of there

Answer

(a, a)

Explanation

Solution

Let circle is x2 + y2 + 2gx + 2fy + c = 0 then g2 = f2 = c also ∣−g+f−a22∣=g2+f2−c\left| \frac{- g + f - a\sqrt{2}}{\sqrt{2}} \right| = \sqrt{g^{2} + f^{2} - c}