center and radius of a circle?

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.

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)

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).

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)

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

X*2+Y*2-10X+2Y+25=0 you ought to get in the format (x+a)^2 + (y+b)^2 = c a and b would properly be ant huge style; c must be constructive regroup (x^2 -10x + 25) + (y^2 + 2y) = 0 upload a million to the two sides to end the sq. (x^2 -10x +25) + (y^2 +2y +a million) = a million (x-5)^2 + (y+a million)^2 = a million center = 5, -a million you get that via fixing (x-5) = 0 x = 5 (y+a million) = 0 y = -a million radius = sqrt of the c term radius =sqrt(c) = sqrt(a million) r = a million

Complete the squares in x and y

For a circle of radius r and centre (x0 , y0) the equation is

(x - x0)^2 + (y -y0)^2 = r^2 ==> x^2 -2x0x +x0^2 + y^2 -2y0y +y0^2 = r^2 ==> x^2 -2x0x + y^2 -2y0y = r^2 + x0^2 + y0^2

And your centre is by comparison x0 = -16/2 = -8 and y0 = -10/2 = -5 ie C: (-8 , -5)

=>x^2+2*8*x+64+y^2+2*5*y+25=85+64+25

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

center is(-8,-5)

radius=sqrt174