Question 11.4.6: Graphing a Hyperbola Centered at (h, k) OBJECTIVE Sketch the...
Graphing a Hyperbola Centered at (h, k)
OBJECTIVE
Sketch the graph of either
\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 or
\frac{(y-k)^{2}}{a^{2}}-\frac{(x-h)^{2}}{b^{2}}=1.
Step 1 Plot the center (h, k) and draw horizontal and vertical dashed lines through the center.
Step 2 Locate the vertices and the endpoints of the conjugate axis. Lightly sketch the fundamental rectangle, with sides parallel to the coordinate axes, through these points.
Step 3 Sketch dashed lines through opposite vertices of the fundamental rectangle. These are the asymptotes.
Step 4 Draw both branches of the hyperbola through the vertices, approaching the asymptotes.
Step 5 Locate the foci on the transverse axis, c units from the center, where
c² = a² + b².
Sketch the graph of each equation.
a. \frac{(x-1)^{2}}{4}-\frac{(y+2)^{2}}{9}=1 . b. \frac{(y+2)^{2}}{9}-\frac{(x-1)^{2}}{4}=1.
