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Question: The equation of the circle which touches both the axes and whose radius is a, is....

The equation of the circle which touches both the axes and whose radius is a, is.

A

x2+y2−2ax−2ay+a2=0x ^ { 2 } + y ^ { 2 } - 2 a x - 2 a y + a ^ { 2 } = 0

B

x2+y2+ax+ay−a2=0x ^ { 2 } + y ^ { 2 } + a x + a y - a ^ { 2 } = 0

C

x2+y2+2ax+2ay−a2=0x ^ { 2 } + y ^ { 2 } + 2 a x + 2 a y - a ^ { 2 } = 0

D

x2+y2−ax−ay+a2=0x ^ { 2 } + y ^ { 2 } - a x - a y + a ^ { 2 } = 0

Answer

x2+y2−2ax−2ay+a2=0x ^ { 2 } + y ^ { 2 } - 2 a x - 2 a y + a ^ { 2 } = 0

Explanation

Solution

Required equation is

(x−a)2+(y−a)2=a2( x - a ) ^ { 2 } + ( y - a ) ^ { 2 } = a ^ { 2 }

⇒x2+y2−2ax−2ay+a2=0\Rightarrow x ^ { 2 } + y ^ { 2 } - 2 a x - 2 a y + a ^ { 2 } = 0.