First slide

Cartesian plane

Question

From a point P, perpendiculars PM and PN are drawn to x and y axes, respectively. If MN passes through fixed point (a,b), then locus of P is

Moderate

A

$xy = ax + by$
B

$xy = ab$
C

$xy = bx + ay$
D

$x + y = xy$

Solution

Let $P (h, k)$
So, points M and N are $(h, 0)$ and $(0, k)$ , respectively.
$MN$ passes through the point $Q (a, b)$
$∴$ So, M,N and Q are collinear.
$∴$ $- \frac{k}{h} = \frac{b - 0}{a - h}$
$∴ ak - hk = - bh$
so locus is $bx + ay = xy$

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