Question

The point which divides externally the line joining the points $(a + b,a - b)$ and $(a - b,a + b)$ in the ratio $a:b$, is.

• A. $\left( \frac{a^{2} - 2ab - b^{2}}{a - b},\frac{a^{2} + b^{2}}{a - b} \right)$
• B. $\left( \frac{a^{2} - 2ab - b^{2}}{a - b},\frac{a^{2} - b^{2}}{a - b} \right)$
• C. $\left( \frac{a^{2} - 2ab + b^{2}}{a - b},\frac{a^{2} + b^{2}}{a - b} \right)$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

Here $x = \frac { a ( a - b ) - b ( a + b ) } { a - b } = \frac { a ^ { 2 } - 2 a b - b ^ { 2 } } { a - b }$

$y = \frac { a ( a + b ) - b ( a - b ) } { a - b } = \frac { a ^ { 2 } + b ^ { 2 } } { a - b }$ .