Question

The locus of points in a plane 1 unit from the point (0,0)

Answer 1

x² + y² = 1

Explanation:

A circle is the locus of a point such that its distance from a fixed point (known as the origin) is always constant. The general equation of a circle is given as:

`(x-h)^2+(y-k)^2=r^2`

Where (h, k) is the center of the circle and r is the radius of the circle.

Given that the plane is 1 unit from the point (0,0). Therefore the radius of the circle is 1 unit and the center of the circle is (0, 0). Therefore the equation of the circle is:

`(x-0)^2+(y-0)^2=1^2\\\\x^2+y^2=1`