Question

What is the foci of an ellipse?

Answer 1

Hint: In this question we have been asked to explain what are the foci of an ellipse. We will first explain what an ellipse is and what are the various properties and features of an ellipse. We will then understand what the foci of an ellipse are and look at the formula to find the coordinates of the focus of an ellipse.

Complete step by step solution:
We all know what a circle is. A circle is shaped which has all the points emerging from a point and joining, which is known as the center. The distance from the center of the circle to the point on the circle is called the radius of the circle.
Similar to circles, we have ellipses which are like circles but which are bent from one side which gives us a shape which instead of a radius, has two segments which are the major axis and the minor axis. The major axis is the longest diameter of the ellipse and the minor axis is the shortest diameter on the ellipse.
Foci are the two points on the major axis of the ellipse such that the sum of the distance of any point on the ellipse from these two points is constant.
Foci are also called as the focus points and have the formula as:
$\Rightarrow F=\sqrt{{{j}^{2}}-{{n}^{2}}}$, where $F$ is the distance between the foci and the ellipse, $j$ is the semi-major axis, which is half of the major axis and $n$ is the semi-minor axis which is the half of the minor axis.
We can see the foci on an ellipse as:

Where $C$ is the center of the ellipse and $A$ and $B$ are the foci of the ellipse.

Note: The equation of an ellipse should be remembered which is given $\dfrac{{{\left( x-h \right)}^{2}}}{{{a}^{2}}}+\dfrac{{{\left( y-k \right)}^{2}}}{{{b}^{2}}}=1$, where $\left( h,k \right)$ is the center of the ellipse, $a$ is the major axis of the ellipse and $b$ is the minor axis of the ellipse. There are two types of ellipse which are vertical ellipse and horizontal ellipse.