# A point moves in a manner that the sum of the squares of its distance from thr origin and the point (2,-3) is always 19.show that the locus of moving point is a circle.find the equation to the circle?

##### 1 Answer

Jul 31, 2018

#### Explanation:

Let the **variable point** be **given fixed points** be

It is given that,

Using the **distance formula,** we have,

**Rewriting** after **completing squares,**

This exhibits that the **locus** of the point is a **circle** having

**centre** at **radius**

It may be **interesting** to **note** that the **centre** of the **circle** is the

**mid-point** of