Image is attached, please help! i’ve been stuck for a while.

Convert the cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation. choices: r4 = -4r2 r2 = 4cos2θ r2 = 4sin2θ

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Find dy/dx using implicit differentiation ln(20+e^xy)=y