center and radius of a circle?

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Factor x and y separately by completing the square:

(x² + 16x) + (y² + 10y) = 85
(x² + 16x + 64) + (y² + 10y + 25) = 85 + 64 + 25
(x + 8)² + (y + 5)² = 174

The center is at (-8, -5) and the radius is about 13.19 units....Show more

Complete the squares:
x^2 +16x +64 +y^2 +10y +25 = 85+ 64+25
(x+8)^2 + (y+5)^2 = 174
So center is at (-8, -5) and radius = sqrt(174)...Show more

You need to complete the square. First rewrite the equation as x^2+16x+64+y^2+10y+25=85+64+25, which reduces to (x+8)^2+(y+5)^2=174. With the equation in this format, you can see that the center of the cirle is (-8,-5), with radius sqrt (174)....Show more

remember the circle equation:

(x - Cx)^2 + (y-Cy)^2 = R^2,
where Cx, Cy is the center, and R is the radius

so you have to convert your equation into something looking like that.

you have

x^2 + 16x, would be nice to have x^2+16x+64, since that's (x+8)^2

likewise, y^2+10y better be y^2+10y+25 = (y+5)^2

so

x^2 + y^2 + 16x + 10y = 85
x^2 + y^2 + 16x + 10y + 64 + 25 = 85 + 64 + 25

(x+8)^2 + (y+5)^2 = 174

so there you have it. The circle is centered at (-8, -5), and its radius is sqrt (174)...Show more

complete square for x and y
to bring it in the standard circle eq. form:
x^2+16x+8^2-8^2 +y^2+10y+5^2-5^2=85
(x+8)^2+(y+5)^2=174
centre= (-8,-5)
radius=√174...Show more