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If $a, x_{1}, x_{2}, x_{3} .....$ and $b, y_{1}, y_{2} ....$ form two infinite A.P’S with common difference p and q respectively then the locus of $P (h, k)$ when $h = \frac{x_{1} + x_{2} + x_{3} .... + x_{n}}{n}, k = \frac{y_{1} + y_{2} + y_{3} .... + y_{n}}{n}$ is

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$q (x - a) = p (y - b)$

$b (x + p) = a (y + q)$

$p (x + a) = q (y + b)$

$p (y + a) = q (x + b)$

answer is A.

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Detailed Solution

$h = \frac{a + p + a + 2 p + ..... + a + n p}{n} h = \frac{n a + p \frac{n (n + 1)}{2}}{n} h = a + \frac{p (n + 1)}{2} k = b + \frac{q (n + 1)}{2} ∴ \frac{h - a}{p} = \frac{k - b}{q}$

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