Identify the equation without completing the square 5x2 6y2

Identify the equation without completing the square. 5x^2 - 6y^2 + 2x - 3y - 5 = 0 A) hyperbola B) ellipse C) circle D) parabola

Solution

5x²-6y²+2x-3y-5=0

5(x²+2x/5 +4/100 -4/100) -6(y²+y/2 +1/4 -1/4)=5

5(x+2/10)²-6(y+1/4)²=5+1/5+3/2=67/10

(x+2/10)²/(67/50) -(y+1/4)²/(67/60)=1

Which is the equation of hyperbola.