极坐标方程4ρsin2θ2＝5化为直角坐标方程是y2＝5x+254y2＝5x+254．

Question

极坐标方程4ρsin2(θ)/(2)＝5化为直角坐标方程是

y2＝5x+(25)/(4)

y2＝5x+(25)/(4)

．

Answer 1

sin²(θ)/(2)=(1−cosθ)/(2)
∴4ρsin2(θ)/(2)＝5化成2ρ（1-cosθ）=5
即2ρ-2ρcosθ=5则2√(x2+y2)−2x＝5
化简得y2＝5x+(25)/(4)
极坐标方程4ρsin2(θ)/(2)＝5化为直角坐标方程是y2＝5x+(25)/(4)
故答案为y2＝5x+(25)/(4)