Question

Equation of the circle passing through $(2,3)$ and centre at the origin is _______ .

• A. $(x-2{)}^2+(y-3{)}^2=13$
• B. $x^2+y^2=13$
• C. $(x-3{)}^2+(y-2{)}^2=13$
• D. $x^2-y^2=13$

Answer 1

The correct option is B

$x^2+y^2=13$

The formula for the equation of a circle is $(x–h{)}^2+(y–k{)}^2=r^2$, where $(h,k)$ represents the coordinates of the centre of the circle, and $r$ represents the radius of the circle.

Given, centre = $(0,0)$ and $(2,3)$ is a point on the circle.

Then the radius '$r$' of this circle is the distance between $(2,3)$ and $(0,0)$.

i.e. $r^2=(3-0{)}^2+(2-0{)}^2=13$

Now, the equation of the circle is,

$(x-0{)}^2+(y-0{)}^2=13$

$⟹x^2+y^2=13$