Question

Write the equation of the circle in general form.

if anyone can explain this that would be great, if not it's okay, just a little lost on how to do all of this haha

Answer 1

`(x +3)^2 + (y-4)^2 = 4`

Explanation:

The general equation of a circle is

`(x-h)^2 + (y-k)^2 = r^2`

In this equation, 'r' represents the radius of the circle and (h,k) represents the central point of the circle.

Radius of the circle is half of the diameter = d/2

From figure, ther diameter of the circle is calculated using (y2-y1) or (x2-x1)

In this figure,

y2 = 6

y1 = 2

d = (y2 - y1) = 6-2 =4

This can also be verified using the values of x

x2 = -1

x1 = -5

d = (x2 - x1) = (-1 - -5) = (-1 + 5) = 4

Also,

r = d/2 = 4/2

r = 2

h represents the horizental distance and k represents the vertical distance of the center of the circle from the origan (0,0).

Therefore,

h = 0 - 3 = -3 as the center of circle is 3 units left to the origan

k = 0 + 4 = 4 as the center of circle is 4 units above to the origan

Therefore the equation of circle becomes

`(x-h)^2 + (y-k)^2 = r^2`

`(x-(-3))^2 + (y-(4))^2 = 2^2`

`(x +3)^2 + (y-4)^2 = 4`