Find the slope of the normal to the curve x = acos3 θ, y = asin3 θ at

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Find the slope of the normal to the curve x = acos3 θ, y = asin3 θ at

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Ruby 2 weeks 2021-10-04T02:35:51+00:00 1 Answer 0 views 0

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    2021-10-04T02:37:27+00:00

    Find the slope of the normal to the curve x = acos³θ, y = asin³θ at θ = π/4

    solution :- x = acos³θ

    differentiate x with respect to θ,

    dx/dθ = 3acos²θ(-sinθ)

    dx/dθ = -3asinθcos²θ ——–(1)

    similarly, y = asin³θ

    differentiate y with respect to θ

    dy/dθ = 3asin²θcosθ ——(2)

    now, dividing equation (2) by (1),

    hence, slope of tangent = -1

    we know, slope of tangent × slope of normal = -1

    so, slope of normal = -1/(slope of tangent)

    = -1/-1 = 1

    hence, slope of normal to the curve = 1

    hope it helps plz mark me as BRILLIANT ❤️❣️….

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