Rectangle ABCD is symmetric with respect to y-axis. Points A and B belong to the parabola y=x2. Points C and D are on the parabola y=−3x2+k. Find k if the area of the rectangle is 66 and length of AB is 6.
AB will be 6 when x = ± 3, that is when y = 9...
I don't have time to do any more but maybe this helps get you started.
Here's a rough drawing (Not to scale):
To continue where hectictar left off......
If AB = 6 then, because we have symmetry with the y axis, B must be the point (3, y)
And y can be found as y = 3^2 = 9
So B = (3, 9)
And because the area of the rectangle is 66 and AB = 6, then BC = 11
Then, C will have the coordinates (3, -2)
So ......using point C and y = -3x^2 + k....we can find k as:
-2 = -3(3)^2 + k
-2 = -27 + k
25 = k
Here's a pic :