Find the standard form for the equation of a circle
(x−h)^2+(y−k)^2=r^2
with a diameter that has endpoints (−8,−10) and (5,−4).
Find the h= -1.5
k= -7
r=?
I do not understand how to find the radius.
just plug in either of the points. They must satisfy the equation, so if we pick (-8,-10),
(-8+1.5)^2 + (-10+7)^2 = r^2
To find the radius of a circle, we can use the distance formula between two points. In this case, the endpoints of the diameter are given as (-8, -10) and (5, -4).
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For our case, the coordinates of the endpoints are (-8, -10) and (5, -4), so:
d = sqrt((5 - (-8))^2 + (-4 - (-10))^2)
= sqrt((13)^2 + (6)^2)
= sqrt(169 + 36)
= sqrt(205)
Therefore, the radius (r) of the circle is the half of the diameter, so the value of r is:
r = sqrt(205) / 2
Hence, the radius of the circle is sqrt(205) / 2, which is approximately 7.15 units.