Find the centre, foci, and eccentricity of the hyperbola
9 36 6 18 0
2 2
x − y − x − y
Answers
Answer:
The hyperbola is centered at the origin, so the vertices serve as the y-intercepts of the graph. To find the vertices, set x=0 x = 0 , and solve for y y . Therefore, the vertices are located at (0,±7) ( 0 , ± 7 ) , and the foci are located at (0,9) ( 0 , 9 ) .
Step-by-step explanation:
The eccentricity of a hyperbola (x - h)2 / a2 - (y - k)2 / b2 = 1 is always greater than 1 and can be calculated using the following formula: e = √(a2 + b2) / a.
actually an ellipse is determine by its foci. But if you want to determine the foci you can use the lengths of the major and minor axes to find its coordinates. Lets call half the length of the major axis a and of the minor axis b. Then the distance of the foci from the centre will be equal to a^2-b^2.