# Finding the radius of a circle in a graph

• newchie
Use the distance formula to express the radius.Now, do you have enough to solve the problem?In summary, a circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r, where p, q and r are integers and are relatively prime. To solve for p+q+r, the vertex of the parabola needs to be determined as (-7/2, + 97/4). The center of the circle is assumed to have the same x coordinate as the vertex and is located at (-7/2, A). The equation for
newchie

## Homework Statement

A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r

## Homework Equations

Vertex form a(x-h)^2+k i believe

## The Attempt at a Solution

So i found the vertex, then i assumed that is one point on the circle, and the other is at (same x,0) then shifted along that but i don't seem to get it of the form sqrtp+q all over r

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I'd suggest trying to use the distance formula for the radius. Not too sure about this but wouldn't the centre of the circle be at the (h,(k/2))? Would you happen to have the answer (from the solution manual or something)?

yes it would be h,k/2
But you get the vertex to be (-97/2,-7/2)
So the radius would just be half the y coordinate, but it doesent really fit the condition of the sqrtp and such part. I think the maximization case i picked is wrong

newchie,
You are assuming that the circle and parabola coincide at the vertex of the parabola. I'm not sure that this is true, although it might be. If the curvature of the parabola at the vertex is greater than the curvature of the circle, the circle won't be inside the parabola, hence won't be inscribed in the parabola.

newchie said:
But you get the vertex to be (-97/2,-7/2)
So the radius would just be half the y coordinate, but it doesent really fit the condition of the sqrtp and such part. I think the maximization case i picked is wrong
No, this isn't where the vertex is - it's at (-7/2, + 97/4).

Yes my error,

Do you have any ideas on how to maximize this I really am stumped o.op

What class are you taking? Is it a calculus class or one that comes before calculus? The type of class you are in will determine the approaches that are available.

Mark44 said:
What class are you taking? Is it a calculus class or one that comes before calculus? The type of class you are in will determine the approaches that are available.

Gr 10, this is a challenge problem. However I know a lot of advanced material, but not calculus, so that won't be helpful :/

newchie said:

## Homework Statement

A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r

## Homework Equations

Vertex form a(x-h)^2+k i believe

## The Attempt at a Solution

So i found the vertex, then i assumed that is one point on the circle, and the other is at (same x,0) then shifted along that but i don't seem to get it of the form sqrtp+q all over r
It looks like you have established the vertex of the parabola as being at (-7/2, 97/4).

It makes sense that the circle with maximal area will be tangent to the parabola at two points, both with the same y coordinate. --- or possibly tangent at only one point if that's the vertex. The maximal circle should also be tangent to the x-axis at x = -7/2, the same x value as the vertex.

Let A be the radius of the circle.

You can assume the center of the circle has the same x coordinate as the vertex of the parabola, namely, -7/2 . Then the center of the circle is at (-7/2, A).

What is the equation for such a circle?

Determine where the circle & parabola intersect.

## 1. What is the formula for finding the radius of a circle in a graph?

The formula for finding the radius of a circle in a graph is r = √(x² + y²), where x and y are the coordinates of the center of the circle.

## 2. How do I determine the radius of a circle if I only have the diameter?

If you only have the diameter of a circle, you can use the formula r = d/2 to find the radius. In this formula, d represents the diameter of the circle.

## 3. Can I find the radius of a circle using the circumference?

Yes, you can find the radius of a circle using the circumference. The formula for this is r = c/2π, where c represents the circumference of the circle and π is the mathematical constant pi.

## 4. Why is it important to find the radius of a circle in a graph?

Knowing the radius of a circle in a graph can help you determine important information about the circle, such as its area and circumference. It can also help you identify the center of the circle and any other key points.

## 5. Can I find the radius of a circle if I only have a portion of the graph?

Yes, you can still find the radius of a circle even if you only have a portion of the graph. As long as you have the coordinates of the center of the circle, you can use the formula r = √(x² + y²) to find the radius.

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