Question

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. $x^2+y^2+10x+10y+25=0$
• B. $x^2+y^2-10x+10y+25=0$
• C. $x^2+y^2+10x-10y+25=0$
• D. $x^2+y^2-10x-10y+25=0$

Answer 1

Answer: (A), (D)

The correct options are
A $x^2+y^2+10x+10y+25=0$
D $x^2+y^2-10x-10y+25=0$


We have, radius $r=5$
The circle is touching both the coordinate axes and center lies on $y=x$, so
$C=(r,r)=(5,5)C^{\prime }=(-r,-r)=(-5,-5)$

Therefore, the possible equations of the circles are
$(x-5{)}^2+(y-5{)}^2=5^2\text{and}(x+5{)}^2+(y+5{)}^2=5^2$
$\Rightarrow x^2+y^2-10x-10y+25=0\text{and}\Rightarrow x^2+y^2+10x+10y+25=0$