Determines the equation of the circumference passing through points A (-2; 0), B (6; 0) and having the center on the line x + 2y + 4 = 0. It then determines the line tangent to the circumference at point A .

y = 4/3 x + 8/3

Step-by-step explanation:

A (-2; 0), B (6; 0) on circle circumference, circle center O (h , k) and radius r

(-2 - h)² + (0 - k)² = r²

(6 - h)² + (0 - k)² = r²

(-2 - h)² = (6 - h)²

4 + 4h + h² = 36 - 12h + h²

16h = 32           h = 2

the center on the line x + 2y + 4 = 0, ∴ 2 + 2y + 4 = 0

y = -3   i.e.  k = -3         center O (2 , -3)

segment OA: (2 , -3) (-2 , 0)

slope OA = (-3 - 0) / (2 - (-2)) = -3 /4

tangent line through A (Lₐ) slope Lₐ = 4/3

y = mx + b    for A(-2 , 0)

b = y - mx = 0 - (4/3 x (-2)) = 8/3

line tangent to the circumference at point A: y = 4/3 x + 8/3

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: