# Points of Intersection of a Hyperbola and a Line

 This is tutorial on finding the points of intersection of a hyperbola and a line given by their equations. Example 1: Find the points of intersection of a hyperbola and a line given by their equations as follows: x2 / 9 - y2 = 1 x + 5y = 3Solution to Example 1: Solve the equation of the line for x to obtain: x = 3 - 5y We now substitute x by 3 - 5y into the equation of the hyperbola to obtain (3 - 5y)2 / 9 - y2 = 1 Expand and group like terms and rewrite the equation as 16y2 -30y = 0 Solve the quadratic equation for y to obtain two solutions y = 0 and y = 15/8 We now substitute the values of y already obtained into x = 3 - 5y to obtain for y = 0, x = 3 and for y = 15/8, x = -51/8 The 2 points of intersection of the the hyperbola and the line are ( 3 , 0) ; ( -51/8 , 15/8) Shown below is the graph of a hyperbola, a line and their points of intersection. More links and references related to the above topics. Equation of Hyperbola- Graphing Problems.