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HyperbolaCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! A Hyperbola is the set of all points P(x, y) in the plane such thatAgain F1 and F2 are focus points. This time the difference of these distances remain a constant at 2a. The explanation is similar to that of the ellipse. Since the ellipse is the sum of the distances and the hyperbola is the difference of the distances, the equations are very similar. They differ only in the sign and the longest side for a hyperbola is c. (Remember for the ellipse it was a) The equation of the above hyperbola is The hyperbola opens left and right. Notice it comes in two parts. Different than an ellipse which is a closed figure. Hyperbolas can also open up and down. So the equation is opposite to that of above hyperbola. If the center of the hyperbola is other than origin. Suppose the center is (h,k) If the hyperbola opens right/left the translation is : If the hyperbola opens up/down the translation is: __________________________________________________________________ 1) Find the coordinates of the vertices, the foci, the eccentricity and the equations of the directrices of the hyperbola 4x ^{2}  25 y ^{2} = 100. (Ans) 2) Find the equation of the hyperbola with vertices at (~+mn~ 5,0) and foci at (~+mn~ 7,0). (Ans) 3) Find the equation of the hyperbola with vertices at (~+mn~ 6,0) and one of the directrix is x = 4. (Ans) 4) Find the coordinates of the vertices, the foci, the eccentricity and the equations of the directrices of the hyperbola 9x ^{2}  16 y ^{2} = 144. (Ans) 5) Find the coordinates of the vertices, the foci, the eccentricity and the equations of the directrices of the hyperbola y ^{2}  16x ^{2} = 16. (Ans) Graph Dictionary Home Covid19 has affected physical interactions between people. Don't let it affect your learning.
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