Find the equation of the ellipse the ends of whose major and minor axes
Question:

Find the equation of the ellipse the ends of whose major and minor axes are (±4, 0) and (0, ±3) respectively.

 

Solution:

Given:

Ends of Major Axis $=(\pm 4,0)$

and Ends of Minor Axis $=(0, \pm 3)$

Here, we can see that the major axis is along the $x-$ axis.

$\therefore$ The Equation of Ellipse is of the form,

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ …(i)

where, a is the semi – major axis and b is the semi – minor axis.

Accordingly, $a=4$ and $b=3$

Substituting the value of $a$ and $b$ in eq. (i), we get

$\frac{x^{2}}{(4)^{2}}+\frac{y^{2}}{(3)^{2}}=1$

$\Rightarrow \frac{x^{2}}{16}+\frac{y^{2}}{9}=1$

 

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