## Question

The extremities of a line segment of length *l* move in two fixed perpendicular straights lines. Find the locus of that point which divides this line segment in ratio 1 : 2.

### Solution

Let *PA* : *PB* = 1 : 2

Squaring and adding equations (i) and (ii) then

∴ Locus of *P*(*h*, *k*) is

#### SIMILAR QUESTIONS

To find the equation of an ellipse from the definition that ellipse is the locus of a point which moves such that the sum of its distances from two fixed points is constant with the fixed points as foci.

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If the angle between the straight lines joining foci and the ends of the minor axis of the ellipse is 90^{o}. Find its eccentricity.

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