 # Conic Sections

Math
Summary

## Problems 3

Summary Problems 3

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

a > b, and 6 > 4. Therefore, a2 is the denominator of the x2 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 9x2 +3y2 - 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 2x2 +3y2 - 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 81x2 + y2 - 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 x2 + y2 - 8x - 16y + 60 = 0?

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