Question

If $\frac{x}{a}$+ $\frac{y}{b}$= 1 and $\frac{x^{2}}{a}$+ $\frac{y^{2}}{b}$= $\frac{ab}{a + b}$ then value of $\frac{x^{n + 1}}{a}$+ $\frac{y^{n + 1}}{b}$ = $\left( \frac{\sqrt{a + b}}{\sqrt{ab}} \right)^{k}$ then relation between n and k.

• A. 2n = k
• B. n = 2k
• C. 2n + k = 0
• D. None

Answer 1

Answer: (C)

2n + k = 0

Answer 2

From (1) equation y = $\frac{b(a - x)}{a}$ put in (2)

we get x = $\frac{ab}{a + b}$, y = $\frac{ab}{a + b}$

Now $\frac{x^{n + 1}}{a}$+ $\frac{y^{n + 1}}{b}$=$\left( \frac{ab}{a + b} \right)^{n + 1}$+ $\left( \frac{ab}{a + b} \right)^{n + 1}$

=$\left( \frac{ab}{a + b} \right)^{n}$= $\left( \frac{\sqrt{a + b}}{\sqrt{ab}} \right)^{- 2n}$

⇒ – 2n = k ⇒ 2n + k = 0