Question

Write the equation for the line tangent to the circle x2 + y2 = 29 at the point (2, 5).

Answer 1

x2 + y2 = 29

Center of the circle
x=0 and y=0

Therefore the slope of the line perpendicular to the tangent line
(y2-y1) / (x2-x1)
(5-0) / (2-0)
5/2

so the slope of the tangent
-2/5

General equation for the line
y = mx + c
if the line satisfies with the point (2,5)
5 = 2m + c

m = -2/5

5 = 2 * (-2/5) + c
c = 5 + (4/5)
c = 29/5

Therefore the equation of the line
y = mx + c
y = (-2/5) m + 29/5