Question

The hyperbola (x-5)^2/7 - (y+3)^2/9 = 1 is shifted to the right by 4 units and upward by 3 units. the new center of the hyperbola is

Answer 1

( 9 ,0)

Explanation:

Given :
`((x -5)^(2))/(7) - ((y+3)^(2))/(9) = 1.` is shifted to the right by 4 units and upward by 3 units

To find : New center of the hyperbola .

Solution : We have given

`((x -5)^(2))/(7) - ((y+3)^(2))/(9) = 1.`

Center of hyperbola is ( 5 , -3)

By the transformation rule f(x) →→ f(x -h) + k it mean f(x) is shifted to right by h unit and k unit up.

Then Center of hyperbola is shifted to the right by 4 units and upward by 3 units.

( 5 , -3) →→ (5 + 4 , -3 + 3

( 5 , -3) →→ ( 9 ,0)

Therefore, new center is ( 9 ,0).

Answer 2

The center of the given hyperbola is (5, -3). Since it is shifted by (4, 3), the new center will be
(5, -3) +(4, 3) = (9, 0)