Question

Equation of the circle with centre on the $y-$axis and passing through the origin and the point $(2,3)$ is

• A. $x^2+y^2+13y=0$
• B. $3x^2+3y^2+13x+3=0$
• C. $6x^2+6y^2-13y=0$
• D. $x^2+y^2+13+3=0$

Answer 1

The correct option is C $6x^2+6y^2-13y=0$

We have to find equation of a circle with center on the y-axis.

General equation of such circle is

$(x-0{)}^2+(y-k{)}^2=k^2$

It passes through $(2,3)$

i.e, $2^2+(3-k{)}^2=k^2$

$\Rightarrow 4+9+k^2-6k=k^2$

$\Rightarrow k=\frac{13}{6}$

$\therefore$ Equation of circle $=x^2+{(y-\frac{13}{6})}^2={\left(\frac{13}{6}\right)}^2$

$=6x^2+6y^2-13y=0$