Question

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=−3x^2+k. Find k if the area of the rectangle is 66 and length of AB is 6.

Answer 1

Notice the picture below

so.. whatever the parabola y= -3x²+k is, will pass over (3,-2) and (-3,-2)

so.. .let us pick say hmmm 3,-2
thus $\bf y=-3x^2+k\qquad \begin{cases} x=3\\ y=-2 \end{cases}\implies -2=-3(3)^2+k$

solve for "k"