2.2 Circles, 2.3 Circles, Finding Intercepts of a Circle

Finding the Intercepts of a Circle (center at the origin)

An x-intercept is where the graph touches or crosses the x-axis.

A y-intercept is where the graph touches of crosses the y-axis.

To find an x-intercept: Let y=0 and solve for x.

To find an y-intercept: Let x=0 and solve for y.

 

Example:  Find the intercepts of the circle for the given equation.

x^2+y^2=25

Solution:

To find an x-intercept, let y=0 and solve for x.

x^2+y^2=25

x^2+(0)^2=25

x^2+0=25

x^2=25

sqrt{x^2}=sqrt{25}

x=pm 5

This equation has two x-intercepts. (5,0) and (-5,0)

To find a y-intercept, let x=0 and solve for y.

x^2+y^2=25

(0)^2+y^2=25

0+y^2=25

y^2=25

sqrt{y^2}=sqrt{25}

y=pm 5

This equation has two y-intercepts. (0,5) and (0,-5)