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For the curve x⁴ + y⁴ = a⁴, a tangent drawn at an arbitrary point meets the coordinate axes at intercepts p and q. Then the quantity p^(-4/3) + q^(-4/3) equals
- a^(-4/3)
- a^(-1/2)
- a^(1/2)
- None of these
Correct answer: a^(-4/3)
Solution
At (x0,y0) the tangent is x*x0^3 + y*y0^3 = a^4, giving x-intercept p=a^4/x0^3 and y-intercept q=a^4/y0^3. Then p^(-4/3)+q^(-4/3) = (x0^4+y0^4)/a^(16/3) = a^4/a^(16/3) = a^(-4/3).
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