# Given that #x# and #y# vary so that #ax + by= c# , where #a,b,c# are constant. Show that the minimum value of #x^2 + y^2# is #c^2/ a^2 + b^2# ?

##### 2 Answers

The minimum value is

#### Explanation:

The minimum of

Then

substituting this value into

Also

#### Explanation:

Let **Origin,** and, **General**

**Point** in the **Plane**

If

a **Family of Lines** in the plane, where,

Let us note that,

Now, the **Distance**

Accordingly, when **Minimum,** so is the **Distance**

Thus, in this new scenario, our **Problem** is to find the

**Minimum Distance** from the **Origin**

From **Geometry,** we know that the minimum distance of a point

them, given by,

Accordingly,

We conclude with a note that, in case,

**Geometrically,** and, in accordance with

**Enjoy Maths.!**