Rectangle ABCD is symmetric with respect to y-axis. Points A and B belong to the parabola y=x^{2}. Points C and D are on the parabola y=−3x^{2}+k. Find k if the area of the rectangle is 66 and length of AB is 6.

Guest Apr 8, 2017

#1**+2 **

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):

hectictar
Apr 8, 2017

#2**+2 **

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 :

CPhill
Apr 8, 2017