Question

Write the equation in standard form for the circle passing through (-3,0 ) centered at theorigin.

Answer 1

x² + y² = 9

Step-by-step explanation

The equation of a circle in standard form is,

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

Where (h, k) is the center of the circle and r is the radius.

In this case, the center is (0, 0), so the equation is,

`x^2+y^2=r^2`

We do not know the radius of the circle, but we know that it passes through (-3, 0), so we can replace x and y with the coordinates of this point to find r,

`(-3)^2+0^2=r^2\text{ }\Rightarrow\text{ }r=√((-3)^2)=3`

Hence, the equation of the circle is x² + y² = 9.