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if x/a +y/b = 2 touches the curve x^n/a^n + y^n/b^n = 2 at the point (m,n) the m and n value will be

if x/a +y/b = 2 touches the curve x^n/a^n + y^n/b^n = 2 at the point (m,n) the m and n value will be

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
the two curve touches each other and hence the gradient at the point (m,n) is same for both
hence
differentiating the second curve we get
x^{n-1}b^n/a^n + y^{n-1}\frac{dy}{dx} = 0
at x =m and y = n, dy/dx = -b/a (gradient of 1st curve)
so putting that and simplifying we get
n/m = b/a
now the point is also on both the curves and thus
m/a + n/b = 2
using these two relations we get the answer as
m = a and n = b

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