10. Find the equation for the ellipse that satisfies the given conditions:

       Vertices (± 5, 0), foci (± 4, 0)

Answers (1)

Given, In an ellipse, 

Vertices (± 5, 0), foci (± 4, 0)

Here Vertices and focus 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.

So on comparing standard parameters( vertices and foci) with the given one, we get 

a=5 and c=4

Now, As we know the relation,

a^2=b^2+c^2

b^2=a^2-c^2

b=\sqrt{a^2-c^2}

b=\sqrt{5^2-4^2}

b=\sqrt{9}

b=3

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.

Exams
Articles
Questions