The equation for an ellipse is (x-h)^2/a^2+(y-k)^2/b^2=1. To identify an ellipse it has both sides squared, its adding and different coefficients. To get the equation is by completing the square. First group the Xs and Ys and move the constant to the other side. Next find the GCF of X and Y and put on the other as well. Then factor both perfect square trinomials and simplify the other side. Finally divide everything by what it equal to get 1 and to reduce the the fractions.
An ellipse looks like a stretch circle because its eccentricity is between 0 and 1. To get the key points of an ellipse it must be in standard form. An ellipse must have its shape skinny or fat, a center, a= with its two vertices and major axis, b= with its two co vertices and minor axis and c with its two foci and eccentricity. If the bigger number lies under x its fat but if it's under y its skinny. The center is (h,k). The major axis is horizontal if the bigger number is under the x term and if its under the y term its vertical. The major axis connects the two vertices together, length of 2a. The minor axis connects the two co vertices together, length of 2b. The focus determines how stretch out is the ellipse, if the focus is closer to zero it makes a circle shape but if its close to one it makes a parabola shape. To find a missing value use the equation c^2=a^2-b^2.
Ellipses are use in the real world like the solar system. Johannes Kepler found out that each planet travels around the sun in an elliptical orbit and the sun being the one foci. This also applies to an atom with the electrons orbiting elliptical and the nucleus being the focus. The lithotripsy, a medical procedure for treating kidney stones and the patient is placed in a elliptical tank of water, with the kidney stone at one focus and high-energy shock waves generated at the other focus are concentrated on the stone, destroying it.
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