
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:
x^{2} / 9  y^{2} = 1
x + 5y = 3
Solution 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  y^{2} = 1
 Expand and group like terms and rewrite the equation as
16y^{2} 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 References and Links to Hyperbolas
Equation of Hyperbola Graphing Problems.
hyperbola equation
Find the Points of Intersection of Two Hyperbolas
Points of Intersection of a Hyperbola and a Line
