NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Graphing hyperbolas with translations

## Interactive practice questions

The graph of the hyperbola $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$(xh)2a2(yk)2b2=1 is the same graph as the graph of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$x2a2y2b2=1, except the center is at $\left(h,k\right)$(h,k) rather than at the origin.

Given the graph of $\frac{x^2}{4}-\frac{y^2}{16}=1$x24y216=1, find the graph of $\frac{\left(x-5\right)^2}{4}-\frac{\left(y-3\right)^2}{16}=1$(x5)24(y3)216=1.

A

B

C

D

A

B

C

D
Easy
Approx a minute

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems