Hyperbola Transformation

1.5

2

3

4

6

8

10

12

5

6

3

4

7.5

Vertical Hyperbola

Vertical Ellipse

Horizontal Hyperbola

Horizontal Ellipse

$$\frac{x^2}{4}-y^2=1$$

$$\frac{x^2}{2}-y^2=1$$

$$\frac{x^2}{4}+y^2=1$$

$$\frac{x^2}{2}+y^2=1$$

3

5

4

6

7.5

(4,22)(4,-2)

(10,16)(10,-8)

(10,14)(10,-6)

(4,20)(4,0)

A hyperbola with vertical asymptote at $$x = 1$$ and horizontal asymptote at $$y = 0$$

A parabola opening upwards with vertex at $$(1, 0)$$

A straight line passing through the origin

A circle centered at $$(1, 0)$$

A hyperbola with vertical asymptotes at $$x = 2$$ and $$x = -2$$ , and horizontal asymptote at $$y = 0$$

A parabola opening upwards with vertex at $$(2, -2)$$

A straight line passing through the points $$(2, 0)$$ and $$(-2, 0)$$

A circle centered at $$(0, 0)$$ with radius 4