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What is the standard form of the equation of an ellipse with center at the origin and a vertical major axis?

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What is the standard form of the equation of an ellipse with center at the origin and a vertical major axis?

Thus, the standard equation of an ellipse is x2a2+y2b2=1. This equation defines an ellipse centered at the origin. If a>b,the ellipse is stretched further in the horizontal direction, and if b>a, the ellipse is stretched further in the vertical direction.

How do you find the general form of an ellipse?

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. �In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.

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How do you find the standard and general equation of an ellipse?

The standard equations of an ellipse are given as,

  1. x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , for the ellipse having the transverse axis as the x-axis and the conjugate axis as the y-axis.
  2. x2b2+y2a2=1 x 2 b 2 + y 2 a 2 = 1 , for the ellipse having transverse axis as the y-axis and its conjugate axis as the x-axis.

What is the length of the latus rectum of an ellipse?

Therefore, the length of the latus rectum of an ellipse is given as: = 2b 2 /a = 2 (2) 2 /3 = 2 (4)/3

Is x^2 a circle or ellipse or hyperbola?

-If the coefficients on x^2 and y^2 match, it is a circle -If there is only one squared term, it is a parabola -If one of the squared terms has a negative coefficient, it is a hyperbola -If the coefficients on x^2 and y^2 don’t match but they still have coefficients that either both positive or both negative, it is a ellipse

What is the difference between a parabola and an ellipse?

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-If there is only one squared term, it is a parabola -If one of the squared terms has a negative coefficient, it is a hyperbola -If the coefficients on x2 and y2 don’t match but they still have coefficients that either both positive or both negative, it is a ellipse This is an ellipse, let’s put in it’s standard form:

How to tell if a graph is a circle or ellipse?

-If the coefficients on x2 and y2 match, it is a circle -If there is only one squared term, it is a parabola -If one of the squared terms has a negative coefficient, it is a hyperbola -If the coefficients on x2 and y2 don’t match but they still have coefficients that either both positive or both negative, it is a ellipse