Finding the points common to a hyperbola and straight line

Question

I'm trying to find points common to hyperbola and straight line. One method is to directly substitute for variables and solve, however it may get tedious, so I'm using parametric form of hyperbola. I've worked my approach but something is wrong as I'm getting 2 possible answers.But in my answer key only one answer is mentioned. Here's my solution.

https://i.stack.imgur.com/WOxrV.jpg

I want to know why extra answer is generated. I'm a newbie to coordinate geometry and sorry, I don't know Latex (so i have to attach a picture)

When you square an equation, you run the risk of introducing extraneous solutions. — amd, Mar 11 '18 at 15:31
Welcome to MSE. Please type your questions (using MathJax) instead of posting links to pictures. — José Carlos Santos, Mar 11 '18 at 15:32
See https://math.stackexchange.com/questions/757497/how-to-solve-4-sin-theta-3-cos-theta-5 — lab bhattacharjee, Mar 11 '18 at 15:56

score 1 · Accepted Answer · answered Mar 11 '18 at 15:32

1

You obtain $25+40\sin\phi+16\sin^2\phi=9\cos^2\phi$ from $5+4\sin\phi=3\cos\phi$. But $5+4\sin\phi=-3\cos\phi$ also implies $25+40\sin\phi+16\sin^2\phi=9\cos^2\phi$.

The extra answer is for $5+4\sin\phi=-3\cos\phi$.

answered Mar 11 '18 at 15:32

CY Aries

23,393

Understood it ! Thanks.... – Shivansh J Mar 11 '18 at 15:37

Finding the points common to a hyperbola and straight line

1 Answers1