# A variable line passing through the origin intersects two given straight lines 2x + y = 4 and x + 3y = 6 at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if?A

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A) OP is the arithmetic mean of OR and OS.

B) OP is the geometric mean of OR and OS.

C) OP is the harmonic mean of OR and OS.

A) OP is the arithmetic mean of OR and OS.

B) OP is the geometric mean of OR and OS.

C) OP is the harmonic mean of OR and OS.

##### 1 Answer

It is quite simple to give an answer in terms of parametric representation for all these curves - a different matter altogether to express them in "standard", i.e.

#### Explanation:

Let the variable line passing through the origin be

The point of intersection

(Substituting

Similarly,

In (A) The point

which is the parametric representation of the locus.

Of course, you can eliminate

The same goes for the other two parts of the question.