Answer to Question #320759 in Geometry for Alina

Question #320759

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.

 

Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x2 + y2 + z2 - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius.

 


 



1
Expert's answer
2022-04-03T15:05:38-0400

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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