Not sure what to solve... I tried to solve it but i ended up proving that it worked.
a. Find the equations of the tangents at C (-2,1) and D (1,2) on the circle x^2+y^2=5
b. Find the point of intersection of the tangents.
~What I did was find the slope and then B, within the formula y=mx+b and then plug that in to x^2+y^2=5 but then it ended up going back to what was already given... so I guess I just don't understand the equation and what's it asking. >.<
you started off the wrong way:
the line joining your two points is not a tangent
you want the tangent line at each of the given points, so there will be two different tangent equations.
That is why it is so important to make a sketch.
Let's just do one of them, for the point (-2,1)
Clearly the tangent at that point must be perpendicular to the radius to that same point.
slope of radius = (0-1)/(0+2) = -1/2
so the slope of the tangent must be +2 ,(the negative reciprocal)
equation of tangent : y = 2x + b
but (-2,1) lies on it, so ...
1 = 2(-2) + b
b = 5
the tangent at (-2,1) is y = 2x + 5
now repeat that for the tangent at the other point
b) you will now have the equation of two straight lines. Use whatever method you normally use to solve two equations in two unknowns