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What is the equation of an ellipse with vertices 2 0 2 4 and foci 2 1 2 3?
Vertices and the foci lie on the line x =2 Major axis is parellel to the y-axis b > a Center of the ellipse is the midpoint (h,k) of the vertices (2,2) Equation of the ellipse is (x - (2) )^2 / a^2 + (y - (2) )^2 / b^2 Equation of the ellipse is (x-2)^2 / a^2 + (y-2)^2 / b^2 The distance between the center and one of the vertices is b The distance between(2,2) and (2,4) is 2, so b = 2 The distance between the center and one of the foci is c The distance between(2,2) and (2,1) is 1, so c = 1 Now that we know b and c, we can find a^2 c^2=b^2-a^2 (1)^2=(2)^2-a^2 a^2 = 3 The equation of the ellipse is Equation of the ellipse is (x-2)^2 / 3 + (y-2)^2 / 4 =1
Does the foci of an ellipse lie on the major axis of the ellipse?
yes
How many lines of symmetry does an ellipse have?
An ellipse has two lines of mirror symmetry: the line that includes the two foci of the ellipse and the perpendicular bisector of the segment of that line between the two foci.
The foci of an ellipse will always lie inside the ellipse true or fale?
true
What do you call a deformed circle?
A randomly deformed circle has no specific name. A circle can be deformed into an ellipse (also known as an oval). An ellipse has two distinct "centres", called foci. The shape consists of the locus of points such that the sum of the distance from these points to the two foci is a constant.
