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Conic Sections

Problems

Ellipses and Circles

Hyperbolas

Problem : Is the major axis of the following ellipse horizontal or vertical: + = 1 ?

a > b , and 6 > 4 . Therefore, a 2 is the denominator of the x 2 term, so the axis is horizontal.

Problem : Find a , b , and c of the ellipse + = 1 .

a = 5 , b = 4 , and c = = 3 .

Problem : Find a , b , and c of the ellipse 9x 2 +3y 2 - 36x - 6y + 12 = 0 .

By completing the square and factoring, you arrive at the standard equation for an ellipse. a = 3 , b = , and c = .

Problem : Find the vertices of the ellipse 2x 2 +3y 2 - 6 = 0 .

a = , the major axis is horizontal, and the center of the ellipse is (0, 0) . The vertices are at (, 0) and (- , 0) .

Problem : What is the eccentricity of the ellipse 81x 2 + y 2 - 324x - 6y + 252 = 0 ?

After completing the square and converting the equation to standard form, you find a = 9 , b = 1 , and c = . Therefore, e = = .

Problem : What is the center and radius of the circle x 2 + y 2 - 8x - 16y + 60 = 0 ?

Center: (4, 8) ; Radius = = 2 .

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