Question

What is the length of the transverse axis of the conic section shown below?

(x+2)^2/16 - (y-3)^2/9 =1

Answer 1

The answer is 8

Explanation:

Just answered

Answer 2

Length of the transverse axis of the given conic section = 8 units.

Explanation:

The equation of hyperbola that has a horizontal orientation in the standard form is;

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

The center is (h, k) , the vertices are
`(h \pm a , k)` and
`(h , k\pm b)`

Since, the vertices are on the hyperbola, but the co-vertices are not on the hyperbola.

• The conjugate axis is the line segment with endpoints at the co-vertices and has length 2b

• The transverse axis is the line segment with endpoints at the vertices and has length 2a.

Since, the equation of the conic section is given as:

`((x+2)^2)/(16) - ((y-3)^2)/(9) = 1`

On comparing with equation [1]

⇒ center = ( -2 , 3 ) and

`a^2 = 16`

`a = √(16) = 4` units

and

`b^2 = 9`

`b = √(9) = 3` units

Length of the transverse axis is the distance between the two vertices, 2a = 2(4) = 8 units.