Find an equation for the circle that has center (-1, 4) and passes through the point (3, -2).
(x - ? )2 + (y - ? )2 = ?
How far apart are the two points? That will be r.
As you know, the circle with center at (h,k) with radius r is
(x-h)^2 + (y-k)^2 = r^2
Now just plug in your numbers.
thats the only info given
Can you not find the distance between two points?
They have given you (h,k). All you need is r.
To find the equation of a circle, you can use the formula:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is given as (-1, 4), and it passes through the point (3, -2).
Step 1: Find the radius (r)
To find the radius, you can use the distance formula between the center of the circle (-1, 4) and the point on the circumference (3, -2).
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, we have:
d = sqrt((3 - (-1))^2 + (-2 - 4)^2)
= sqrt(4^2 + (-6)^2)
= sqrt(16 + 36)
= sqrt(52)
= 2*sqrt(13)
So, the radius (r) is 2*sqrt(13).
Step 2: Plug the values into the equation
Now that we have the center (-1, 4) and the radius 2*sqrt(13), we can substitute these values into the equation:
(x - h)^2 + (y - k)^2 = r^2
Substituting, we get:
(x - (-1))^2 + (y - 4)^2 = (2*sqrt(13))^2
(x + 1)^2 + (y - 4)^2 = 52
Therefore, the equation of the circle that has a center (-1, 4) and passes through the point (3, -2) is:
(x + 1)^2 + (y - 4)^2 = 52