Question

Write the equation of the circle with center (0,0) and (-1,-3) a point on the circle

Answer 1

Equation of given circle :- x² + y² = 4

Explanation:

The equation of the circle with center (0, 0) and radius r is given by,

x² + y² = r²

It is given that, a circle with center (0,0) and (-1,-3) a point on the circle

To find the radius of circle

radius r = √[(0 - - 1)² + (0 - -3)²] =√(1 + 3) =√4 = ±2

r = 2

To find the equation of circle

x² + y² = r²

x² + y² = 2²

x² + y² = 4

Answer 2

`\left(x\right)^2+\left(y\right)^2=10`

Explanation:

Given that center of the circle is at (0,0) and it passes through a point (-1,-3).

Now we need to write the equation of the circle with given center and point on the circle.

So let's plug given values into standard formula of the circle

`\left(x-h\right)^2+\left(y-k\right)^2=r^2`

there (h,k) gives center of the circle then h=0, k=0

So we get equation :

`\left(x-0\right)^2+\left(y-0\right)^2=r^2`

`\left(x\right)^2+\left(y\right)^2=r^2` ...(i)

plug the given point (-1,-3) that is x=-1 and y=-3 into (i)

`\left(-1\right)^2+\left(-3\right)^2=r^2`

`1+9=r^2`

`10=r^2`

plug above value into (i)

`\left(x\right)^2+\left(y\right)^2=10`

Hence final answer is
`\left(x\right)^2+\left(y\right)^2=10`