Solve 4c=1+4r^2: HSC Advanced Maths Exam Ques.

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Homework Statement


http://www.mediafire.com/?rhnyop6erds34db

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

Homework Equations



given*

The Attempt at a Solution


I have no idea ):
 

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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.
 
hscguy said:

Homework Statement


http://www.mediafire.com/?rhnyop6erds34db

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

Homework Equations



given*

The Attempt at a Solution


I have no idea ):

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.
 
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