Question

Identify all the hyperbolas which open horizontally

Answer 1

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

and

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

Explanation:

There are 2 types of hyperbolas:

Horizontal:

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

Vertical:

`((y-k)^2)/(a^2)-((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

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

and

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

Answer 2

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

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