
This is a tutorial with detailed solutions to problems related to the ellipse equation. An HTML5 Applet to Explore Equations of Ellipses is also included in this website. ReviewAn ellipse with center at the origin (0,0), is the graph ofThe length of the major axis is 2a, and the length of the minor axis is 2b. The two foci (foci is the plural of focus) are at (± c , 0) or at (0 , ± c), where c^{2} = a^{2}  b^{2}. Problem 1Given the following equation9x^{2} + 4y^{2} = 36 a) Find the x and y intercepts of the graph of the equation. b) Find the coordinates of the foci. c) Find the length of the major and minor axes. d) Sketch the graph of the equation. Solution to Example 1 a) We first write the given equation in standard form by dividing both sides of the equation by 36 and simplify 9 x^{2} / 36 + 4 y^{2} / 36 = 1 x^{2} / 4 + y^{2} / 9 = 1 x^{2} / 2^{2} + y^{2} / 3^{2} = 1 We now identify the equation obtained with one of the standard equation in the review above and we can say that the given equation is that of an ellipse with a = 3 and b = 2 NOTE: a > b Set y = 0 in the equation obtained and find the x intercepts.
x^{2} / 2^{2} = 1
Set x = 0 in the equation obtained and find the y
intercepts.
Matched Problem: Given the following equation 4x^{2} + 9y^{2} = 36 a) Find the x and y intercepts of the graph of the equation. b) Find the coordinates of the foci. c) Find the length of the major and minor axes. d) Sketch the graph of the equation. More Links and References on EllipsesCollege Algebra Problems With Answers  sample 8: Equation of EllipsePoints of Intersection of an Ellipse and a line HTML5 Applet to Explore Equations of Ellipses Find the Points of Intersection of a Circle and an Ellipse Ellipse Area and Perimeter Calculator Find the Points of Intersection of Two Ellipses 