Conic Sections

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

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

Solution for Problem 2 >>

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

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

Solution for Problem 3 >>

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

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

Solution for Problem 4 >>

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

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

Solution for Problem 5 >>

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

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

Solution for Problem 6 >>

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

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