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aisha
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When in standard form how do you know whether the ellipse is horizontal or vertical? and how do you know what a= and b= for the major and minor axis, and vertices? How do you get the coordinates of the foci?
The standard form of an ellipse is (x - h)2/a2 + (y - k)2/b2 = 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, respectively.
The standard form of an ellipse is a simplified version of the general form, which is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. In the standard form, the coefficients A and C are equal and B = 0, making it easier to identify the center and axes of the ellipse.
The standard form of an ellipse tells us that it is a symmetrical, closed curve with a center point and two axes, representing the widest and narrowest points of the ellipse. The ratio of a to b also indicates the elongation or flattening of the ellipse.
To graph an ellipse using the standard form, we first plot the center point (h,k). Then, we move a units horizontally and b units vertically from the center to plot the endpoints of the semi-major and semi-minor axes. We can then use these points to sketch the ellipse.
Yes, we can convert an ellipse from standard form to general form by expanding the squared terms and simplifying the equation. This can be useful when solving systems of equations or finding the equation of a tangent line to the ellipse.