Points of Intersection of a Hyperbola and a Line
This is tutorial on finding the points of intersection of a
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 = 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 - 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.
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