Convert the polar equation to rectangular form r2 4 sin2 th

Convert the polar equation to rectangular form. r^2 = 4 sin(2 theta)

Solution

given r²  = 4 sin(2t)

r² = 8 sint cost

r⁴ = 8 rsint rcost

now convert into rectangular form

x=rcost ,y =rsint

r² = x² + y²

(x² + y²)² = 8 xy

  x² + y² = 2 sqrt(2xy)