identify the curve represented by the equation

Question

identify the curve represented by the equation: 4x(x-3) = 2x^2 -2y^2 +5

sketch and label all its properties.

Answer 1

4x^2-12x=2x^2-2y^2+5

 

(2x^2-12x)+2y^2-5=0

 

2(x-3)^2-5-18+2y^2=0

 

(x-3)^2+y^2=[sqrt(23/2)]^2

 

This is the equation of a circle.

Center is (3,0)

 

Radius = sqrt(23/2)