Question

Identify all the hyperbolas which open horizontally

Answer 1

Answer:

The hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Step-by-step explanation:

A hyperbola with equation of the form:

(x-h)^2/a^2-(y-k)^2/b^2)=1 opens horizontally

Then, the hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Answer 2

Answer:

$\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1$

and

$\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1$

Step-by-step explanation:

There are 2 types of hyperbolas:

Horizontal:

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

Vertical:

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$

If the x term is positive then parabola is horizontal.

If the y term is positive then parabola is vertical.

so, only first two equations are in which x term is positive.

hence, equations are

$\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1$

and

$\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1$