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.

Answers (1)
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 bare 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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