Question

Find the center and radius of the circles. $2 x^{2}+2 y^{2}-x=0$

Answer 1

Hint: 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.

Complete step by step solution:
Given the equation of the circle is
$2 x^{2}+2 y^{2}-x=0$
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.
$\text { or, } x^{2}+y^{2}-\dfrac{x}{2}=0$
$\text { or, } x^{2}-2 \cdot x \cdot \dfrac{1}{4}+\dfrac{1}{4^{2}}+y^{2}=\dfrac{1}{4^{2}}$
$\text { or, }\left(x-\dfrac{1}{4}\right)^{2}+y^{2}=\dfrac{1}{4^{2}}$
From this equation we've the center is $\left(\dfrac{1}{4}, 0\right)$ and radius is $\dfrac{1}{4}$.

Note: The general equation of a circle is another name for the center of 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.
The group of points whose separation from a fixed point has a constant value are represented by a circle. The radius of the circle, abbreviated $r$, is a constant that describes this fixed point, which is known as the circle's centre. The formula for a circle$\left(\mathrm{x}-\mathrm{x}_{1}\right)^{2}+\left(\mathrm{y}-\mathrm{y}_{1}\right)^{2}=\mathrm{r}^{2}$ whose centre is at $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$