How to find the equation of curves which pass through the intersection of two curves whose equations are given? i am stuck at these type of questions. Dont know what is the short method.

For these type of questions, you have to use a parameter A to find the equation of the desired curve.
If the two curves are given as f(x) and g(x), and we have to find the equation of a curve which passes through the intersection of these curves, write the equation of desired curve as :
f(x) + A g(x) = 0
Now, there may be given some other conditions, put them into this equation and find out the value of A. Now you have the value of A, you have the equation of curve.
THanks