Question

The equation of the circle touching the $y-$axis whose radius is $5$ units and $y-$coordinate of the centre is $-7,$ is

• A. $x^2+y^2-10x+14y+49=0$
• B. $x^2+y^2+10x+14y+49=0$
• C. $x^2+y^2+10x+14y+25=0$
• D. $x^2+y^2-10x+14y+25=0$

Answer 1

Answer: (A), (B)

$x^2+y^2+10x+14y+49=0$

Given : Circle touches the $y-$axis and the radius is $5\text{units}$, so the centre of the circle is
$C=(\pm 5,-7)$
So, the equation of the circle is
$(x\pm 5{)}^2+(y+7{)}^2=5^2$
$\Rightarrow x^2+y^2-10x+14y+49=0$
And $x^2+y^2+10x+14y+49=0$