This question appeared in my practise exam and I didn't have a clue of how to go about it... here goes...

If S (a,b) represents the coordinates of the focus for conic x^2 + 2xy + y^2 +2x + 4y = 0, then the maximum value of |a|.b is
a) 1
b) 2
c) 3
d) 4

It'd be great if someone would help me with the solution and provide me with a detailed explanation... thanks

Solving for y, we get:

y=\sqrt{2(x+2)}-x-2

Find the derivative and set to 0. Solve for x.Sub back in to find the y coordinate.

These correspond to (a,b).

Then, plug them into |a|*b to find the max value.

Thank You very much...