1. Find the equation of the asymptotic of the hyperbole
x^2/9 - y^2/ 4 = 1.
2. Given the equation of a function 2x^2 + 5y^2 - 16x + 20y + 108 =0, translate the original so that the New equation will have no first degree terms.
2. Find the radius and the polar coordinates of the center of the circle r=2cos theta - 2square root of 3 sine theta.
the asymptotes are always y=±(b/a)x
2x^2 + 5y^2 - 16x + 20y + 108 =0
2x^2-16x + 5y^2+20y + 108 = 0
2(x^2-8x) + 5(y^2+4y) + 108 = 0
2(x^2-8x+16) + 5(y^2+4y+4) + 108 - 2(16) - 5(4)
2(x-4)^2 + 5(y+2)^2 + 56 = 0
I suspect a typo, since the above equation has no real solutions.
r = 2cosθ - 2√3 sinθ
r^2 = 2rcosθ - 2√3 rsinθ
x^2+y^2 = 2x - 2√3 y
x^2-2x + y^2+2√3 y = 0
x^2-2x+1 + y^2+2√3 y + 3 = 1+3
(x-1)^2 + (y+√3)^2 = 4
Now you can easily answer the questions.