What is the equation of a circle whose diameter endpoints are at 2 -3 and 8 7 on the Cartesian plane and what are the tangent equations touching its endpoints showing work?

Endpoints: (2, -3) and (8, 7)

Centre of circle: (5, 2)

Radius of circle is the square root of 34

Equation of the circle: (x-5)^2 +(y-2)^2 = 34

Slope of radius: 5/3

Slope of tangents: -3/5

1st tangent equation: y--3 = -3/5(-2) => 5y = -3x-9

2nd tangent equation: y-7 = -3/5(x-8) => 5y = -3x+59