Question

The equation of a circle whose radius is $8$ units and which touches both $x-$axis and $y-$axis is

• A. $x^2+y^2-16x-16y+64=0$
• B. $x^2+y^2+16x-16y+64=0$
• C. $x^2+y^2+16x+16y+64=0$
• D. $x^2+y^2-16x+16y+64=0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $x^2+y^2-16x-16y+64=0$
B $x^2+y^2+16x-16y+64=0$
C $x^2+y^2+16x+16y+64=0$
D $x^2+y^2-16x+16y+64=0$

Radius of the circle $=8$ units.
Since, the circle touches both $x-$axis and $y-$axis, the centre of the circle will be $(8,8),(-8,8),(-8,-8),(8,-8)$.
The required equation of the circle whose radius is $8$ units and touches both $x$-axis and $y$-axis is
$(x-8{)}^2+(y-8{)}^2=8^2$
$\Rightarrow x^2-16x+64+y^2-16y+64=64$
$\Rightarrow x^2+y^2-16x-16y+64=0$

Similarly,
$(x+8{)}^2+(y-8{)}^2=8^2$
$\Rightarrow x^2+y^2+16x-16y+64=0$
$(x+8{)}^2+(y+8{)}^2=8^2$
$\Rightarrow x^2+y^2+16x+16y+64=0$
$(x-8{)}^2+(y+8{)}^2=8^2$
$\Rightarrow x^2+y^2-16x+16y+64=0$