Question

Find an equation of a line tangent to a circle X^2+y^2=10

at (-1. 3).

Answer 1

Its the line perpendicular to the radius that goes to (-1, 3).

Answer 2

If you wanna to it via calculus, implicit is the way to go.

Answer 3

the center of the circle is (0, 0) and the point of tangency is (-1, 3).
the slope of the radius to the point of tangency is perpendicular to the line tangent at (-1, 3). slope of the radius is -3. so the slope of the tangent line is 1/3.

so the equation of the tangent line is y-3=3(x+1)

Answer 4

y = (1/3)(x+1) + 3
Got your slope mixed up there.