Answer:
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
