Question

Equation of a circle whose center is origin and radius is equal to the distance between the lines ${x}=1$ and ${x}=-1$ is

Answer 1

Hint: The radius of a circle is the length of the straight line that connects the center to any point on its circumference. Because a circle's circumference can contain an endless number of points, a circle can have more than one radius. This indicates that a circle has an endless number of radii and that each radius is equally spaced from the circle's center. When the radius's length varies, the circle's size also changes.

Complete step by step solution:
Distance between lines ${x}=1$ and ${x}=-1$
$r-2$ units
The center of a circle is a location inside the circle that is situated in the middle of the circumference.The radius of a circle is the constant distance from the circle's center to any point on the circle.A circle's diameter is defined as the segment of a line that connects two locations on the circle and passes through its center.
center , $0 \equiv({h}, {k}) \equiv(0,0)$
Equation: $(x-h)^{2}+(y-k)^{2}=r^{2}$
The general equation of a circle is another name for the center of the circle formula. If the radius is r, the center's coordinates are $(h,k),$and any point on the circle is$(x, y)$, the center of the circle formula is as follows:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
The equation for the center of the circle is another name for this. In the sections that follow, we'll use this formula to determine a circle's equation or center.
$(x-0)^{2}+(y-0)^{2}=2^{2}$
$\therefore x^{2}+y^{2}=4$

Note: A circle's center and radius make up its 2D shape. If we are aware of the circle's center and radius, we can draw any circle. The radii of a circle are infinitely variable. The midpoint where all of the radii meet is the center of a circle. The center of the circle's diameter is another way to describe it.