Question

The circle C has equation

Answer 1

Answer:

$y=-4x+12\\y =-0.421x+12$

Step-by-step explanation:

The lines through (0,12) would have equation of the form

y = mx+12

If this is tangent, the distance of centre from the tangent = radius of the circle

Distance of (6,5) ie centre from tangent line is

$\frac{6m+7}{\sqrt{1+m^2} } =\sqrt{17} \\(6m+7)^2 = 17(1+m^2)$

$36m^2+84m+49 =17+17m^2\\19m^2+84m+32=0$

m=-4,-0.421

Hence tangents are

$y=-4x+12\\y =-0.421x+12$