Question

Show that the equation 3x²+3y2 +12x+18y-11=0 represent a circle​

Answer 1

3x²  + 3y²  + 12x  + 18y   - 11  =0 is an equation of circle

Step-by-step explanation:

Equation of a circle  is

(x - h)² + (y - k)² = r²

3x²  + 3y²  + 12x  + 18y   - 11  =0

Dividing both sides by 3

=> x² + y²  + 4x + 6y - 11/3 = 0

=> x²  + 4x  +  y² + 6y  = 11/3

=> x² + 4x + 4 - 4  + y² + 6y  + 9 - 9  = 11/3

=> (x + 2)² + (y + 3)² = 13 + 11/3

=> (x + 2)² + (y + 3)² = 50/3

=> (x + 2)² + (y + 3)² = 5² * 2 / 3

=> (x -(-2))² + (y - (-3))² = (5√2 / √3)²

Center = ( - 2 , - 3)

radius = 5√2 / √3

Hence 3x²  + 3y²  + 12x  + 18y   - 11  =0 is an equation of circle

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