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

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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.

 


 

 

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