Question

Find the centre and radius of the circle
3x²+3y²-6x+4y-1

Answer 1

Answer:

3x²+3y²-6x+4y-1 = 0

(÷3) x²+y²-2x+4/3y-1/3 = 0

x²-2x+1-1+y²+4/3y+2/√3-2/√3-1/3 = 0

(x²-2x+1)+(y²+4/3y+2/√3)-(1+2/√3+1/3) = 0

(x-1)²+(y+2/√3)² = (3+2√3+1)/3

= (4+2√3)/3

(x-1)²+(y+2/√3)² = 2/3(2+√3) (1)

(1) is in the form of (x – h)² + (y – k)² = r²

h = 1, k = -2/√3

centre of the circle,

(h, k) = (1,-2/√3)

r² = [2/3(2+√3)]²

= 4/9(4+3+4√3)

= 4/9(7+4√3)