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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