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

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In summary, the conversation is discussing a question from the HSC Advanced Maths exam in Australia, which involves finding the equation for the intersection points between a circle and a parabola. The question also refers to a given stipulation and asks for a condition that the discriminant and sum of the roots of a quadratic equation must satisfy.
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hscguy
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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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  • #2
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
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.
 
Last edited:

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

How do you solve 4c=1+4r^2?

To solve this equation, we need to isolate the variable "r" on one side of the equation. We do this by dividing both sides of the equation by 4 and then taking the square root of both sides. This will give us the value of "r".

What is the value of "c" in 4c=1+4r^2?

To find the value of "c", we can substitute the value of "r" that we found in the previous step into the equation. This will give us a numerical value for "c".

Can this equation be solved using the Quadratic Formula?

Yes, this equation can be solved using the Quadratic Formula. We can rearrange the equation to be in the form ax^2+bx+c=0 and then use the formula to find the values of "r".

What does "HSC" stand for in this question?

"HSC" stands for Higher School Certificate, which is an academic qualification in New South Wales, Australia. This type of question is typically found in the HSC Advanced Maths exam.

Are there any restrictions on the values of "c" and "r" in this equation?

Yes, there are some restrictions on the values of "c" and "r" in this equation. Since we are taking the square root of both sides, the value inside the square root (1+4r^2) must be greater than or equal to 0. This means that "r" cannot be a negative number. Additionally, "c" and "r" must be real numbers, meaning they cannot be imaginary or complex numbers.

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