I have a circle, centre (-3,2) and radius of sqr root 10. The question is asking me to find the equation of the tangent at (-2,5)....

What is the slope of the line containing the center and the point of tangency?

What is a basic property of tangents? That is, at what sort of "angle" does a tangent touch a circle? So what is the relationship between the line through the center and the tangency point, and the tangent line?

Then what is the slope of the tangent line?

Then what is the equation of the tangent?

A circle is tangent to the y-axis at y=3 and has one x-intercept at x=1. Determine the other x-intercept.

Since the circle is perpendicular to the y-axis, what is the y-coordinate of the center?

You have the equation (x - h)

^{2} + (y - 3)

^{2} = r

^{2}. You have the points (0, 3) and (1, 0) on the circle. Plug these into the equation. See where the resulting equations lead you....