Question

Find the value of k so that the straight line 4 x+3 y+k = 0 may touch the circle x^2+y^2-4 x+10 y = 4.

Answer 1

cente C=(2,-5)

radius r=root 33

tangent condition is r=d

where d is the distance of the line from centre

$\sqrt{33} = \frac{4(2) + 3( - 5) + k}{ \sqrt{ {4}^{2} + 3 {}^{2} }}$

$\sqrt{33} = \frac{8 - 15 + k}{5} = \frac{k - 7}{5}$

$k = 7 + 5 \sqrt{33}$