20 + 4a^2/9 = a^2
20 + 4a^2 = 9a^2
An ellipse is a type of geometric shape that resembles a flattened circle. It has a curved perimeter and two focal points, which are equidistant from the center of the ellipse.
The equation of an ellipse with b=3 and center at M(-2√5,2) can be found using the standard form of the ellipse equation:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h,k) is the center of the ellipse and a and b are the lengths of the semi-major and semi-minor axes. Plugging in the given values, we get the equation:
(x+2√5)^2/9 + (y-2)^2/3 = 1
b represents the length of the semi-minor axis of the ellipse. It is half the length of the minor axis, which is the shorter diameter of the ellipse. It helps determine the shape and size of the ellipse.
To graph an ellipse with the equation (x+2√5)^2/9 + (y-2)^2/3 = 1, first find the center point at (-2√5,2). Then, plot the two points on the major axis by adding and subtracting the length of the semi-major axis (3) from the x-coordinate of the center point. Next, plot the two points on the minor axis by adding and subtracting the length of the semi-minor axis (2) from the y-coordinate of the center point. Finally, sketch the ellipse through these points.
An ellipse and a circle are different types of geometric shapes. A circle has a constant distance from the center to any point on its perimeter, while an ellipse has varying distances from the center to points on its perimeter. Additionally, a circle has a single radius, while an ellipse has two radii – one for the semi-major axis and one for the semi-minor axis.