Find the equation (formula) of a circle with radius r and center C(h,k) and if the Center of a circle is at (3,-1) and a point on the circle is (-2,1) find the formula of the circle.
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Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x2Â + y2Â + z2Â - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius.
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The equation of the circle:
"(x-h)^2+(y-k)^2=r^2"
"C(h,k)=(3,-1)"
Point: "(-2;1)" .
"(-2-3)^2+(1-(-1))^2=r^2"
"25+4=r^2"
"r=\\sqrt {29}"
the equation of the circle:
"(x-3)^2+(y+1)^2=29" .
The equation of the sphere:
"(x-h)^2+(y-k)^2+(z-l)^2=r^2"
"x^2 + y^2 + z^2 - 6x + 2y + 8z - 4 = 0"
"(x^2 -6x+9)-9+ (y^2 +2y+1)-1+""( z^2+8z+16)-16 -4=0"
"(x-3)^2+(y+1)^2+(z+4)^2-30=0"
The equation of the sphere
"(x-3)^2+(y+1)^2+(z+4)^2=30" .
The centre of the sphere:
"C(h,k,l)=(3,-1,-4)" .
Radius:
"r=\\sqrt {30}" .
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