Math help +REP

[Teabags]

Really just starting to annoy me now.

"Find the equations of the tangent of this circle: (x-1)^2 + (y+2)^2 = 13; (3,1)"

[Pieman]

Find the derivative (Using implicit differentiation). It will give you:

y' = -(x-1)/(y+2)

Plug in the points, done.

Using your coordinates should be, the slope of the tangent line should be: -2/3

[Pieman]

Typo;
"Using your coordinates, ..." is what it should be.

[Soka]

Is this a C1 question or C3? Find the gradient of the circle by implicit differentiation as Pieman said. If your stuck on implicit differentiation you should see your teacher.

You will then get, as pieman said dy/dx = -(x-1)/(y+2)

Next put in the given coordinates (3,1) giving the gradient of the circle as -2/3 at this point.

Now you know that tangents to a circle have the same gradient at that point (from C1). You can then use either of:
y = mx + c OR y-1 = m(x-3) to get the line of the tangent, where m is the gradient.