Q. 1 E5.0( 1 Vote )

# Find the angle to

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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