what is the equation if a circle, in standared form, that has a diameter with endpoints at (-4,3) and (0,-5)?

Question

i dont know how to do this someone help i have to turn this in by tomorrow or i fail. so if you know it please tell me! :)

Answer 1

The diameter of the circle is the distance between (-4,3) and (0,-5).

d=√(16+64)=√80=4√5; the center is (-2, -1) [the midpoint of (-4,3) and (0,-5)].The radius is r=2√5.

So the equation of the circle is

(x+2)²+(y+1)²=20

 

Answer 2

Okay, don't panic! Let's start with the equation of a circle:

(X - h)² + (Y - k)² = r²

We need the center and the radius, and have neither. However, remember that the diameter is twice the radius because it passes through the center. That means the center of your diameter is the center of the circle. We only need the midpoint:

(-4 + 0) / 2  ,  (3 - 5) / 2

  -4 / 2  ,  -2 / 2

     -2  ,  -1

Okay, so there we have h and k. To get the radius, we need the distance from that center to either point:

d = √[( -2 - 0)² + (-1 - -5)²

  = √[ (-2)² + (4)²]

  = √[ 4 + 16]

  = √ 20

In other words, that is our radius. We would normally simplify that, but we don't need to this time:

(X - -2)² + (Y --1)² = (√20)²

(X + 2)² + (Y + 1)² = 20

 

 

Answer 3

You need help with English grammar as well as math!

 

The co-ordinates of the center of the circle are (-2, -1).  The square of the radius of the circle is is 20.

 

The circle is (x+2)² + (y+1)² = 20.

 

These are the answers.  Can you figure out how they were obtained?