Question

How do I know whether the major axis of an ellipse is horizontal or vertical?

Answer 1

In this question, they have asked that when do we say the major axis of an ellipse is horizontal or vertical. To explain this question, first we have to give some definitions and then we have to give one example and with the use of our example we have to tell when we say that the major axis of an ellipse is horizontal or vertical. Basically, we can tell this by looking at the denominator of the given equation of the ellipse.

Complete step by step answer:
The major axis in a horizontal ellipse is given by the equation $y = v$ . The major axis in a vertical ellipse is represented by $x = h$ .
Whenever a denominator is larger, it determines which variable is a major axis. Always $a$ is the major axis. If the larger number is under the $X$ , then the ellipse is horizontal. If the larger number is under the $Y$ , then the ellipse is vertical.
Equation of an ellipse is $\dfrac{{{X^2}}}{{{a^2}}} + \dfrac{{{Y^2}}}{{{b^2}}} = 1$ …. (1)
Suppose $a$ is greater than $b$ $\left( {i.e\,.,a > b} \right)$ in the equation (1) then the major axis of an ellipse is horizontal. Since $a$ is the denominator of $X$ .
Suppose $b$ is greater than $a$ $\left( {i.e.,\,b > a} \right)$ in the equation (1) then the major axis of an ellipse is vertical. Since $b$ is the denominator of $Y$ .

Note: Let us see the example for the major axis being horizontal. Let us take an equation of ellipse as $\dfrac{{{X^2}}}{{25}} + \dfrac{{{Y^2}}}{9} = 1$ , here the major axis is $X$ , then the ellipse is horizontal.
Let us see the example for the major axis being vertical. Take the equation of an ellipse as $\dfrac{{{X^2}}}{9} + \dfrac{{{Y^2}}}{{25}} = 1$ , here the major axis is $Y$ , then the ellipse is vertical.