# 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?

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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

**A) :**

#### Explanation:

Let us name the given **lines**

Let the **variable line** through the **Origin** be

Suppose that **Axis.**

Clearly,

Now, for any **distance**

Given that,

and, since

But,

Recall that to find the **Locus** of **conds.**

**A),B),C),** we have to **establish algebraic relation** btwn.

using **A),B),C).**

**Part A) :** **AM** of

Under this cond.,

Then, by

Returning to **traditional** **desired locus** is given by,

**Parts B) and C)** can be **dealt** with **similarly.**

**Enjoy Maths.!**