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

     Major axis on the x-axis and passes through the points (4,3) and (6,2).

Answers (1)

Given, in an ellipse

Major axis on the x-axis and passes through the points (4,3) and (6,2).

Since The major axis of this ellipse is on the  X-axis, 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.

Now since the ellipse passes through the point,(4,3)

\frac{4^2}{a^2}+\frac{3^2}{b^2}=1

{16b^2+9a^2}={a^2b^2}

since the ellipse also passes through the point (6,2).

\frac{6^2}{a^2}+\frac{2^2}{b^2}=1

4a^2+36b^2=a^2b^2

On solving this two equation we get

a^2=52 and b^2=13

Thus, The equation of the ellipse will be 

\frac{x^2}{52}+\frac{y^2}{13}=1

Exams
Articles
Questions