Q. 1 E5.0( 1 Vote )

Find the angle to

Answer :

Given:


Curves + 1 ...(1)


& x2 + y2 = ab ...(2)


Second curve is x2 + y2 = ab


y2 = ab – x2


Substituting this in equation (1),


+ 1


1


x2b2 + a3b – a2x2 = a2b2


x2b2 – a2x2 = a2b2 – a3b


x2(b2 – a2) = a2b(b – a)


x2


x2


x2


a2 – b2 = (a + b)(a – b)


x ...(3)


since , y2 = ab – x2


y2 = ab – ()


y2


y2


y = ± ...(4)


since ,curves are + 1 & x2 + y2 = ab


Differentiating above w.r.t x,


. = 0


. =




m1 ...(5)


Second curve is x2 + y2 = ab


2x + 2y.0


m2 ...(6)


Substituting (3) in (4), above values for m1 & m2,we get,


At (, ) in equation(5),we get





m1


At (, ) in equation(6),we get





m2


when m1 & m2



tanθ


tanθ


tanθ


tanθ


tanθ


tanθ


tanθ


θ = tan – 1()


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