Find the equation of the tangent line to the circle with center at (-3,1), at point (-2,5). Write the answer in general form.

Question

Write answer in general form. Thank you!

Answer 1

The equation of the circle has the form (x+3)²+(y-1)²=a² where a is the radius.

The circle must pass through (-2,5), so 1²+4²=17=a².

The equation is (x+3)²+(y-1)²=17.

Differentiating we get 2(x+3)+2(y-1)dy/dx=0, dy/dx=-(x+3)/(y-1).

The tangent is dy/dx so at (-2,5), dy/dx=-1/4.

Tangent line is y-5=-(x+2)/4=-x/4-1/2, y=-x/4+9/2.