# Diameter of a circle endpoints P(0,0) Q(8,-4) what equation:

• Jaco Viljoen
In summary, to find the equation of a circle with endpoints P(0,0) and Q(8,-4), first find the midpoint at (-4,-2) and then use the formula r^2=(x-h)^2+(y-k)^2 to find the radius. The equation would be (x-4)^2+(y+2)^2=20.
Jaco Viljoen
Mod note: Moved from technical math section, so no template.
The diameter of a circle has endpoints P(0,0) and Q(8,-4) Find the equation:

First I will find the midpoint:
$$M(x,y)=(x1+x2)/2,(y1+y2)/2$$
$$=8/2,-4/2)$$
$$M(x,y)=(-4,-2)$$

Then I will find the radius:
$$r^2=(x-h)^2+(y-k)^2$$
$$r^2=(0-4)^2+(0+2)^2$$
$$r^2=16+4$$
$$r^2=20$$

so
$$(x-4)^2+(y+2)^2=20$$

Last edited by a moderator:
Jaco Viljoen said:
The diameter of a circle has endpoints P(0,0) and Q(8,-4) Find the equation:

First I will find the midpoint:
$$M(x,y)=(x1+x2)/2,(y1+y2)/2$$
$$=8/2,-4/2)$$
$$M(x,y)=(-4,-2)$$

Then I will find the radius:
$$r^2=(x-h)^2+(y-k)^2$$
$$r^2=(0-4)^2+(0+2)^2$$
$$r^2=16+4$$
$$r^2=20$$

so
$$(x-4)^2+(y+2)^2=20$$
That's what I get, as well.

BTW, this looks like homework, or at least a problem from a textbook, so I'm moving it to the homework section.

Jaco Viljoen
Thank you Mark,
I wasn't sure if I should post under pre calculus as I couldn't find any geometry there, thanks again.

This would come under the heading of analytic geometry, so the Precalc section is the right place for it.

Jaco Viljoen

## 1. What is the equation for finding the diameter of a circle with endpoints P(0,0) and Q(8,-4)?

The equation for finding the diameter of a circle with endpoints P(0,0) and Q(8,-4) is d = √((x2-x1)^2 + (y2-y1)^2), where x1 and y1 are the coordinates of endpoint P and x2 and y2 are the coordinates of endpoint Q.

## 2. How do you calculate the diameter of a circle using coordinates?

To calculate the diameter of a circle using coordinates, you can use the distance formula d = √((x2-x1)^2 + (y2-y1)^2), where x1 and y1 are the coordinates of one endpoint and x2 and y2 are the coordinates of the other endpoint.

## 3. Can the diameter of a circle be negative?

No, the diameter of a circle cannot be negative. The diameter is a measure of the length of a line segment connecting two points on the circle, and length cannot be negative.

## 4. What is the significance of the diameter of a circle?

The diameter of a circle is an important measurement that helps in determining the size, area, and circumference of a circle. It is also used in various mathematical and scientific calculations, such as in finding the volume of a cylinder.

## 5. How can the equation for finding the diameter of a circle be derived?

The equation for finding the diameter of a circle can be derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. By applying this theorem to a circle with endpoints P(0,0) and Q(8,-4), we can find the distance between the two points, which is the diameter of the circle.

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