# 18. Find the equation for the ellipse that satisfies the given conditions:       b = 3, c = 4, centre at the origin; foci on the x axis.

P Pankaj Sanodiya

Given,In an ellipse,

b = 3, c = 4, centre at the origin; foci on the x axis.

Here  foci of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.

Therefore, the equation of the ellipse will be of the form:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Where $a$ and $b$are the length of the semimajor axis and semiminor axis respectively.

Also Given,

$b=3$ and $c=4$

Now, As we know the relation,

$a^2=b^2+c^2$

$a^2=3^2+4^2$

$a^2=25$

$a=5$

Hence, The Equation of the ellipse will be :

$\frac{x^2}{5^2}+\frac{y^2}{3^2}=1$

Which is

$\frac{x^2}{25}+\frac{y^2}{9}=1$.

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