Which is a focus of the hyperbola shown?

(−20, 0)
(−24, 0)
(25, 0)
(30, 0)

The distance from the center to the focus is the same as the distance from the center to the corner of the dashed green rectangle shown (not to scale). The hypotenuse of a rectangle with legs 7 and 24 is √(49+576) = 25, so the distance will be 25 from (0, 0) to the focus at (25, 0).

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-03-21T15:48:45+01:00

The focus of the hyperbola is at (25, 0)

From the figure, the legs of the dashed line are:

7 units long and 24 units long.

So, we start by calculating the leg of the diagonal (d) using the following Pythagoras theorem.

[tex]d = \sqrt{x^2 + y^2}[/tex]

So, we have:

[tex]d = \sqrt{7^2 + 24^2}[/tex]

Evaluate

[tex]d = 25[/tex]

Given that the center of origin of the hyperbola is at the center of the dashed line, it means that the distance will be 25 from (0, 0) to the focus at (25, 0).

Hence, the focus of the hyperbola is at (25, 0)

Which is a focus of the hyperbola shown? (−20, 0) (−24, 0) (25, 0) (30, 0)

Respuesta :

Otras preguntas

Which is a focus of the hyperbola shown?

(−20, 0)
(−24, 0)
(25, 0)
(30, 0)