Question

tangent to 3x-4y-18=0 with radius 10 and center at a pt on 4x+3y+1=0

Answer 1

how would you define a line perp to 3x-4y = 18 ?

Answer 2

Just to see what is going on, I would plot the 2 lines
it sounds like they want a circle with its center on one of the lines
and at a point where the radius will be 10 and just touch the first line.

as amistre pointed out, the radius will be perpendicular to the first line

Answer 3

there will be 2 points in the solution set

Answer 4

Let (x1,y1) be the centre.
Perpendicular distance from centre to tangent =radius
we find an equation in x1,y1
also( x1,y1) lies on line 4x+3y+1=0
we get two equations in x1,y1,solve and find value of x1,y1