Find the area of the loop of the curve x(x^2+y^2)=a(x^2-y^2).
Find the area of the loop of the curve x(x^2+y^2)=a(x^2-y^2).
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If tanθ=tanhxcoty and tanϕ=tanhxtany , prove that sin2θ/sin2ϕ=(cosh2x+cos2y)/(cosh2x-cos2y)
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Solve the differential equation by removing the first derivative d^2y/dx^2-4xdy/dx+(4x^2-3)y=e^x^2
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Find the envelope of the family of the curves x^2/cos^2α+y^2/sin^2α=a^2-b^2, where α is the paramete
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Prove that the condition that the plane ux+vy+wz=0 may cuts rhe cone ax^2+by^2+cz^2=0 in perpendicu
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