The equation(s) of the circle(s) having radius 5, centre on the line y=x and touching both the coordinate axes is(are)
A
x2+y2+10x+10y+25=0
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B
x2+y2−10x+10y+25=0
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C
x2+y2+10x−10y+25=0
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D
x2+y2−10x−10y+25=0
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Solution
The correct options are Ax2+y2+10x+10y+25=0 Dx2+y2−10x−10y+25=0 We have, radius r=5 The circle is touching both the coordinate axes and center lies on y=x, so C=(r,r)=(5,5)C′=(−r,−r)=(−5,−5)
Therefore, the possible equations of the circles are (x−5)2+(y−5)2=52 and (x+5)2+(y+5)2=52 ⇒x2+y2−10x−10y+25=0 and ⇒x2+y2+10x+10y+25=0