Question

Do the problem in the attached file.

Answer 1

implicit differentiation
\[2x + 2yy' = 0\]\[m=y'=6\]\[2x +12y=0\]\[x=-6y\]substitute to the circle equation to find the point\[\left( -6y \right)^{2}+y^{2}=592\]\[37y^{2} = 592\]\[y=\pm4\]we choose y = -4 for the blue line\[x=24\]the equation of the line:\[y+4=6\left( x-24 \right)\]\[y=6x-148\]

Answer 2

Excellent