The coordinates of the center of the ellipse is (-1,-2), the value 'a' in the equation is 3 and the value of b is 4.
The equation of the ellipse is the equation which is used to represent the ellipse in the algebraic equation form with the value of center point in the coordinate plane and measure of minor and major axis.
The standard form of the equation of the ellipse can be given as,
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
Here (h,k) is the center of the ellipse, (a) is the major axis and (b) is the length of minor axis.
The coordinates of the ellipse shown in the figure is 2 units below x-axis and 1 units left to the y-axis in the third quadrant. Thus, the coordinates of the center of the ellipse is (-1,-2)
The value 'a' in the equation is the distance from the center to a vertex of an ellipse. (The point furthest from the center).
This is also known as the major axis. The distance of point (1,-2) from center of ellipse is "a" which is 3 units.
[tex]a=3[/tex]
The value 'b' in the equation is the distance from the center to a co-vertex of an ellipse. (The point closest from the center).
This is also known as the minor axis of ellipse. The distance of point (0,1) from center of ellipse is "b" which is 2 units.
[tex]b=2[/tex]
Put the values in the equation of ellipse as,
[tex]\dfrac{(x-(-1))^2}{3^2}+\dfrac{(y-(-2))^2}{2^2}=1\\\dfrac{(x+1)^2}{9}+\dfrac{(y+2)^2}{4}=1[/tex]
This is the required equation of ellipse.
Thus, the coordinates of the center of the ellipse is (-1,-2), the value 'a' in the equation is 3 and the value of b is 4.
Learn more about the equation of ellipse here;
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