Thread: [SOLVED] Hyperbola AGAIN :S

A, B are points on the x-axis, y-axis respectively. If OA = a, OB = b, what are the coordinates of P, the midpoint of AB? If the line AB moves so that the area of the triangle OAB is always 2c^2, find the locus of P. Show that the line AB touches the locus of AB.

Alright so i've found the midpoint = (a/2, b/2). But how exactly do I find its locus with the fact about the area of the triangle???

Please help?

Originally Posted by UltraGirl

A, B are points on the x-axis, y-axis respectively. If OA = a, OB = b, what are the coordinates of P, the midpoint of AB? If the line AB moves so that the area of the triangle OAB is always 2c^2, find the locus of P. Show that the line AB touches the locus of AB.

Alright so i've found the midpoint = (a/2, b/2). But how exactly do I find its locus with the fact about the area of the triangle???

Please help?

When the line AB moves within the co-ordinate axis, its length remains constant. To have the constant area, length of the perpendicular from the origin must remain constant.
So find the equation of the straight line AB and length AB. Find the perpendicular distance p from the origin. Then
A = 1/2*AB*p = 2c^2.