Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Intersection of a line and an ellipse
Replies: 2   Last Post: Sep 16, 2009 7:42 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Scales

Posts: 187
From: Australia
Registered: 4/3/05
Re: Intersection of a line and an ellipse
Posted: Aug 22, 2009 6:23 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi Walter,

Express the equation of

the line in the form y = m*x + d...(1)

and the equation of the ellipse in the form

(x-xc)^2/a^2 + (y-yc)^2/b^2 = 1...(2)

Substitute y from (1) into (2) and solve for the two values of x-coord.

Then from (1) get x = (y-d)/m , substitute this into
(2) and solve for the two y-coord values.

Both these equations will have sqrt terms, as you are solving quadratics.
If the value under the sqrt is zero, then both values are equal, and the line is tangent to the ellipse.
If the value under the sqrt is negative, then there are no real solutions as the line does not intersect the ellipse.

Regards, Peter Scales.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2015. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.