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Find the coordinates of the center of the ellipse represented by 4x^2 + 9y^2 – 18y – 27 = 0.

For 2x^2 + xy + 2y^2 = 1, find , the angle of rotation about the origin, to the nearest degree.

Find the distance between points at (–1, 6) and (5, –2).

Identify the conic section represented by x^2 – y^2 + 12y + 18x = 42.

Find the coordinates of the points of intersection of the graphs of x^2 + y^2 = 5, xy = –2, and y = –3x + 1.

• Pre-calculus HELP PLEASE ! -

4x^2 + 9(y^2-2y+1) = 27+9
4x^2 + 9(y-1)^2 = 36
x^2/9 + (y-1)^2/4 = 1
so, the center is at ...

2x^2 + xy + 2y^2 = 1
cot2θ = (A-C)/B
so θ=

d^2 = (5+1)^2 + (-2-6)^2
d = ...

x^2 – y^2 + 12y + 18x = 42
(x^2+18x+81) - (y^2-12y+36) = 42+81-36
(x+9)^2 - (y-6)^2 = 87
so, it's a ...

solving the equations in pairs, we get
(-2,1),(-1,2),(-2/5,11/5),(1,-2),(2,-1)

• Pre-calculus HELP PLEASE ! -

(2/9, -1 2/4)

?

d=10

ellipse

?

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