Question

In the following equations, which axis is the transverse axis and what are the intercepts:

4y² - 25x² = 100?

Answer 1

The transverse axis of the hyperbola given by the equation 4y² - 25x² = 100 is the y-axis after the equation is rearranged to its standard form. There are no x-intercepts, and the y-intercepts are (0, 5) and (0, -5).

Step-by-step explanation:

The equation 4y² - 25x² = 100 represents a hyperbola. To identify the transverse axis and the intercepts, we'll first rearrange the equation into its standard form. Dividing both sides by 100, we get:
(y/5)² - (x/2)² = 1

In this form, it's clear that the y-term is positive and the x-term is negative, indicating that the transverse axis is along the y-axis. The intercepts can be found by setting each variable to zero in turn:

• For the x-intercepts, set y to 0, which results in no solution since a negative number cannot be equal to 1.
• For the y-intercepts, set x to 0, which gives y = ±5. This means there are two y-intercepts at (0, 5) and (0, -5).

Thus, the transverse axis is the y-axis, and the intercepts are (0, 5) and (0, -5).