x^2+y^2-10x+8y+32=0 
Write the equation in standard form.
State the center, radius, and intercepts.
Submit the graph

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center of the circle, r is the radius, and x and y are the intercepts.

x^2 + y^2 + (-10)x + 8y = -32

Complete the squares.

x^2 + (-10)x = (x + -5)^2 - 25

y^2 + 8y = (y + 4)^2 - 16

Substitute into standard form.

(x + -5)^2 - 25 + (y + 4)^2 - 16 = -32

Add 25 and 16 to both sides. 

Standard form:  (x + -5)^2 + (y + 4)^2 = 9

The center of the circle is (5, -4) and the radius is 3.


 

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial