Question

Which hyperbolas have one vertex in common with the hyperbola (y−4)² ?

a) (x+1) ² −(y−4)² =16
b) (x−3)² +(y−4)² =25
c) (x+2)² −(y−4)² =9
d) x−5)² +(y−4)² =36

Answer 1

The hyperbola (y−4)² has one vertex in common with the hyperbola given by the equation (x−3)² +(y−4)² =25.

Step-by-step explanation:

To determine which hyperbolas have one vertex in common with the hyperbola (y−4)², we need to compare the equations of the hyperbolas and identify any similarities.

Let's go through each option:

1. (a) (x+1)² −(y−4)² =16
2. (b) (x−3)² +(y−4)² =25
3. (c) (x+2)² −(y−4)² =9
4. (d) (x−5)² +(y−4)² =36

After comparing, we find that option (b) has one vertex in common with the hyperbola (y−4)², making it the correct answer.