Pre-calc question

Question

A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius at the point of contact. Which an equation in point-slope form for the line tangent to the circle whose equation is 𝑥^2 + 𝑦^2 = 25 at the point(3, −4)

Answer 1

slope of the perpendicular line through (3,-4) and the origin is (0- -4)/(0-3) = -4/3

slope of the tangent line is the negative inverse = 3/4

equation of the tangent line is y+4 = (3/4)(x-3) or

4y+16 =3x-9 or

4y=3x-25

Answer 2

The slope of the radius at (3,-4) is -4/3 and the perpendicular has slope 3/4

3/4=(y+4)/(x-3) is the equation of the tangent line.

You make the point slope form from this equation.