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Question: The equations of the circles touching both the axes and passing through the point (1, 2) are....

The equations of the circles touching both the axes and passing through the point (1, 2) are.

A

x2+y2−2x−2y+1=0,x2+y2−10x−10y+25=0x ^ { 2 } + y ^ { 2 } - 2 x - 2 y + 1 = 0 , x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 25 = 0

B

x2+y2−2x−2y−1=0,x2+y2−10x−10y−25=0x ^ { 2 } + y ^ { 2 } - 2 x - 2 y - 1 = 0 , x ^ { 2 } + y ^ { 2 } - 10 x - 10 y - 25 = 0

C

x2+y2+2x+2y+1=0,x2+y2+10x+10y+25=0x ^ { 2 } + y ^ { 2 } + 2 x + 2 y + 1 = 0 , x ^ { 2 } + y ^ { 2 } + 10 x + 10 y + 25 = 0

D

None of these

Answer

x2+y2−2x−2y+1=0,x2+y2−10x−10y+25=0x ^ { 2 } + y ^ { 2 } - 2 x - 2 y + 1 = 0 , x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 25 = 0

Explanation

Solution

Equation of circle touching both the axes will be x2+y2−2ax−2ay+a2=0x ^ { 2 } + y ^ { 2 } - 2 a x - 2 a y + a ^ { 2 } = 0

Also it passes through (1, 2), therefore a=5,1a = 5,1.

Hence the equations of circles are

x2+y2−2x−2y+1=0x ^ { 2 } + y ^ { 2 } - 2 x - 2 y + 1 = 0 and x2+y2−10x−10y+25=0x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 25 = 0.