# Homework Help: Show that 4c=1+4r^2

1. Dec 11, 2012

### hscguy

1. The problem statement, all variables and given/known data
http://www.mediafire.com/?rhnyop6erds34db

This was a question from the HSC Advanced maths exam in Australia, the second easiest maths course.
2. Relevant equations

given*

3. The attempt at a solution
I have no idea ):

2. Dec 11, 2012

### symbolipoint

An idea to start is to solve the system for x and y, even though they will be in symbolic form. Notice, that in i, what you are asked to show is not expressed with x or y.

3. Dec 11, 2012

### Curious3141

Find the equation that gives the solution set for the intersection points between the circle and the parabola. This is a quartic in x, reducible to a quadratic in x2. Now use the stipulation given ("located symmetrically") to deduce a condition that the discriminant of that quadratic must satisfy.

For the second part, figure out what condition the sum of the roots of that quadratic has to satisfy.

Last edited: Dec 11, 2012