Question

Find the equation of the circle with centre at
(12,5) and touching the line 3x - 4y + 9 = 0​

Answer 1

Answer:

Standard equation of a circle with center at (h, k) and radius R is:

(x - h)² + (y - k)² = R²

In this case the given center is at: (h, k) = (12, 5), so all we need to find is the

length of the radius, now when a circle touches a line then that line is tangent to

circle which means the radius is perpendicular to tangent line at the point they

touch, we can use the following formula:

Distance(shortest) between line: Ax + By + C = 0, and point(x₁ , y₁) is:

d= |Ax₁ + By₁ + C|/√(A² + B²) , therefor in this case:

R = |3*12 + (-4*5) + 9|/√[(3² +(-4)²]

R = |36 - 20 + 9|/√(9 + 16)

R = 25/5 = 5