We do the midpoint formula to find the center of the circle to get the left side of the equation.
Midpoint = [(X₁ + X₂) / 2 , (Y₁ + Y₂) / 2]
Now plug in:
[(8 + 4) / 2 , (- 6 - 2) / 2]
(12 / 2 , - 8 / 2)
(6, - 4)
The center of the circle is (6, -4)
Now we plug it into the equation of a circle:
(x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
(x - 6)² + (y + 4)² = r² is the left side of the equation. This will eliminate options A and C
Now we do the distance formula using the center and an endpoint to get the radius. The formula for distance is:
√((X₂ - X₁)² + (Y₂ - Y₁)²)
We plug in using either of the endpoints.
√((4 - 6)² + (- 2 - (- 4))²)
√((-2)² + 2²)
√(4 + 4)
√8
√8 is your radius
(√8)² = 8
Your correct answer is (x - 6)² + (y + 4)² = 8, Option D
Answer:
y = 
x + 
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)
m = 
= , hence
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 5 ), then
5 = + c ⇒ c = 5 - =
y = x + ← in slope-intercept form
Answer: It's the top left because the line passes through 10 on the y axis.
The answer is there are no solution that fulfill this equation because if you put for example -14 the answer will be -8 but there is absolutely sign, so the answer is 8. Hope it help!
