First slide

Equation of line in Straight lines

Question

P, Q,R and S are the points of intersection with the coordinate axes of the lines $p x + q y = p q$ and $q x + p y = p q$ , then $(P, Q > 0)$

Easy

A

P,Q,R,S form a parallelogram
B

P,Q,R,S form a rhombus
C

P,Q,R,S are concyclic
D

P,Q,R,S form square

Solution

If the point of intersection of two lines with coordinate axes be concylic, then product of intercepts on the x-axis is equal to product of intercepts on y-axis by these lines.
This is a geometric property.

The intercepts on x- axis are p and q and whose product is pq.

Also, the intercepts on y-axis are p, and q, whose product is also pq.

Hence, the four points are concylic.

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