Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 9 } = 1$ is shifted horizontally and vertically to obtain the hyperbola $\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$.
Graph the new hyperbola.

Question

Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 9 } = 1$ is shifted horizontally and vertically to obtain the hyperbola $\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$.   
Graph the new hyperbola.

Quizplus · Accepted Answer

Comparing the given equation with the general equation $\frac {(x-h)^2}{a^2}-\frac {(y-k)^2}{b^2}=1$ of a hyperbola, we get $h=0$, $k=0$, $a=8$ and $b=3$.

Thus, the center of the original hyperbola is at $(0,0)$ and the distance between center and vertices is $a=8$ along the x-axis and the distance between the center and the co-vertices is $b=3$ along the y-axis.

To shift the center of the hyperbola by $(2,-1)$, we need to subtract 2 from x-coordinate and add 1 to the y-coordinate of each point on the hyperbola. So, we get the equation of the new hyperbola as $\frac {(x+2-2)^2}{8^2}-\frac{(y-1+1)^2}{3^2}=1$, which simplifies to $\frac {(x)^2}{64}-\frac{(y)^2}{9}=1$.

Thus, the new hyperbola has the same shape and size as the original hyperbola but shifted 2 units to the left and 1 unit up.

The correct graph is shown in choice A.

Solve the Problem x264−y29=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 9 } = 164x2​−9y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 9 } = 1$