find the equations of two straight lines drawn through the point(0,a) on which the perpendicular let fall from the point (2a,2a) are each of length a.

Write the general equation in the form of slope intercept with m1 and m2 as the slopes of the 2 lines. These both lines have the intercept as ‘a’. Equate the length of perpendicular from (2a, 2a) to ‘a’ to get the value of m1 and m2.
Substitute in gen. eqn to get the answer