Given:
Four different equations are given
Required:
To tell Which equation represents a circle?
Explanation:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis this means it touches the x-axis at that point
[tex]\begin{gathered} \frac{x^2}{2^2}+\frac{y^2}{2^2}=1 \\ \\ x^2+y^2=2^2 \\ \\ so\text{ r =2} \end{gathered}[/tex]
That is others are in the form of ellipse equation.
How do you find the general form of an ellipse?
The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
else three options resemble with ellipse equation
Required answer:
[tex]\frac{x^{2}}{2^{2}}+\frac{y^{2}}{2^{2}}=1[/tex]
