Solving A System of Linear-Quadratic Equations

Question

The diagram shows a circle with the equation x^2 + y^2 = 25. Algerbraically prove that the line with equation 3x + 4y = 0 is tangent to the circle, and determine the point of contact.

Answer 1

x^2+y^2 = 25

3x +4y=0 is not a tangent line

it runs right through the center of the circle

3x+4y =25 is tangent at (3,4)

3x+4y =-25 is tangent at (-3,-4)

3x+4y = 0 is parallel to the 2 tangent lines midway between them