Heart - Touching Lines

Heart is

Find the equation of the straight lines touching lines both x^2+y^2=2a^2 and y^2=8ax .

The equation of the circle touching the lines |y| = x and having radius sqrt(2) is :

Equation of circle touching the lines |x-2| + | y-3|=4 will be

Consider the following statements: (i) Infinitely many circles can be drawn touching two parallel lines.( ii).Exactly four circles can be drawn touching two intersecting lines.(iii). Exactly one circle can be drawn touching three lines,not being concurrent.The true statements are:

Differential equation of the family of circles touching the line y=2 at (0,2) is

If y=f(x) be the equation of the line touching the line y=2x+3 " at " x=2 , then

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Property 3: The equation of the family of circles touching the circles and line at their point of contact is