Question

please solve this as fast as possible
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Answer 1

you should know ,

slope of normal and slope of tangent are perpendicular to each other.

e.g., slope of normal × slope of tanngent..

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refer to the attachment

x = 1 - a sinθ

differentiate x with respect to θ,

dx/dθ = 0 - a.d(sinθ)/dθ = - a.cosθ ------(1)

y = bcos²θ

differentiate y with respect to θ,

dy/dθ = b. d(cos²θ)/dθ

= b. 2cosθ. (-sinθ)

= -2bsinθ.cosθ --------(2)

dividing equations (2) by (1),

dividing equations (2) by (1),

dy/dx = -2bsinθ.cosθ/-acosθ = 2b/a sinθ

at θ = π/2 , dy/dx = 2b/a sinπ/2 = 2b/a

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

= -1/(2b/a) = -a/2b