Page 82 - Calculus for the Clueless, Calc II
P. 82
Just like with the ellipse, let's clarify the location of the vertices. In this case, the vertices occur north-south of
the center (-7,6). So the x value of the vertices is the same as the center, x = -7. Substituting, we get
The vertices are (-7,6 ± 5 ).
1/2
For the same reason, the foci, always on the axis through the vertices, are (-7,6 ± 22 ). The asymptotes and the
1/2
sketch are the same!!
Example 13—
Sketch and discuss 25X - 4y + 50x - 12y + 116 = 0.
2
2
For the last time, we will complete the square, again a little bit differently.
Center (-1,-3/2); vertices ; foci ; asymptotes .
Sometimes we have a puzzle. Given some information, can we find the equation? You must always draw the
picture and relate the picture to its equation.
