Question

Write the standard equation of the circle with center (– 10, –3) that passes through the point (-3,3).

Answer 1

Answer:

$(x+10)^2 + (y+3)^2 = 85$

Step-by-step explanation:

Equation of a circle:

The standard equation of a circle with center $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In which r is the radius.

Center (– 10, –3)

This means that $x_0 = -10, y_0 = -3$. So

$(x - x_0)^2 + (y - y_0)^2 = r^2$

$(x - (-10))^2 + (y - (-3))^2 = r^2$

$(x+10)^2 + (y+3)^2 = r^2$

Passes through the point (-3,3).

This means that we use $x = -3, y = 3$ to find the radius squared. So

$(x+10)^2 + (y+3)^2 = r^2$

$(-3+10)^2 + (3+3)^2 = r^2$

$r^2 = 49 + 36$

$r^2 = 85$

The equation of the circle is:

$(x+10)^2 + (y+3)^2 = r^2$

$(x+10)^2 + (y+3)^2 = 85$