
This is tutorial on finding the points of intersection of an ellipse and a line given by their equations.
Example 1Find the points of intersection of an ellipse and a line given by their equations as follows:We first solve the equation of the line for y to obtain: y = 2 x  2 We now substitute y by 2x  2 in the equation of the ellipse x^{2} / 9 + (2 x  2)^{2} / 4 = 1 Multiply all terms by 36, group like terms and rewrite the equation as 40 x^{2}  72 x = 0 Solve the quadratic equation for x to obtain two solutions x = 0 and x = 9/5 We now substitute the values of x already obtained into the equation y = 2x  2 and find y. for x = 0, y = 2 and for x = 9/5, y = 8/5 There 2 points of intersection given by ( 0 , 2) and (9/5 , 8/5) The graphs of the ellipse and the line given by their equations above and their points of intersection are shown below.
More Links and References on EllipsesFind the Points of Intersection of two EllipsesFind the Points of Intersection of a Circle and an Ellipse Equation of Ellipse, Problems. College Algebra Problems With Answers  sample 8: Equation of Ellipse HTML5 Applet to Explore Equations of Ellipses Ellipse Area and Perimeter Calculator 