For the curve 4x^5=5y^4, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is

Question

Accepted Answer

Correct answer: D. (d) : 4x^5=5y^4 ⇒ 4x^55=y^4 ⇒ 4x^45y^4= 1x ⇒ x^4y^4= 54x Diff. w.r.t. x we get 4 5x^45=4y^3y^ ' ⇒4x^4=4y^3y^ ' ⇒ dy dx= x^4y^3 length of sub tangent at (x ,y )= yx^4/y^3= y^4x^4 length of sub normal =y dy dx=y x^4y^3= x^4y^2 Req. ratio = ( y^4x^4 )^3/ ( x^4y^2 )^2 = y^12x^12 y^4x^8= y^16x^20= ( y^4x^4 )^4 1x^4 = ( 45x )^4 1x^4= ( 45 )^4

$For the curve 4 x^{5} = 5 y^{4}, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is$

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