Name: Different Forms of a Parabola
Uploaded: 2019-07-19
Duration: 5 min 32 s
Description: What is the Equation of a parabola? Do different equations look different on the graph? What are some of the points associated with a parabola?

Question

The equation of an ellipse is $\frac{x^{2}}{4} + \frac{y^{2}}{36} = 1$ . Find

Length of the major axis = _____units.

Length of the minor axis =_____units.

Coordinates of its vertices are $A$ (_____) and $B$ (_____).

Coordinates of its foci are $F_{1}$ (_____) and $F_{2}$ (______).

Eccentricity, $e =$ _____.

Length of the latus rectum =_____units.

Accepted Answer

Given equation is $\frac{x^{2}}{4} + \frac{y^{2}}{36} = 1$

This is of the form $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$ , where $a^{2} > b^{2}$ .

So, it is an equation of a vertical ellipse.

Here $(a^{2} = 36 \Rightarrow a = 6)$ and $(b^{2} = 4 \Rightarrow b = 2)$ .

$∴ c = \sqrt{a^{2} - b^{2}} - \sqrt{36 - 4} = 4 \sqrt{2}$ .

Thus, $a = 6, b = 2, c = 4 \sqrt{2}$ .

Length of the major axis $= 2 a = 12$ units.

Length of the minor axis $= 2 b = 4$ units.

Coordinates of its vertices are $A (0, - a)$ and $B (0, a)$ , i.e., $A (0, - 6)$ and $B (0, 6)$ .

Coordinates of its foci are $F_{1} (0, - c)$ and $F_{2} (0, c)$ , i.e., $F_{1} (0, - 4 \sqrt{2})$ and $F_{2} (0, 4 \sqrt{2})$ .

Eccentricity, $e = \frac{c}{a} = \frac{4 \sqrt{2}}{6} = \frac{2 \sqrt{2}}{3}$ units

Length of the latus rectum $= \frac{2 b^{2}}{a} = \frac{(2 \times 4)}{6} = \frac{4}{3}$ units

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

The equation of an ellipse is x24+y236=1. Find Length of the major axis = _____units. Length of the minor axis =_____units. Coordinates of its vertices are A(_____) and B(_____). Coordinates of its foci are F1(_____) and F2(______). Eccentricity, e=_____. Length of the latus rectum =_____units.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !