Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Conic Sections
0 votes

Find the equation of an ellipse that satisfies the following conditions: Major axis on x-axis, passes through the points $(4,3)$ and $(6.2)$

Can you answer this question?

1 Answer

0 votes
  • Given an ellipse as follows:
  • http://clay6.com/mpaimg/Toolbar_7.png
  • The equation of the ellipse is $\large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2}$$=1$
  • $c= \sqrt {a^2 - b^2}$
  • Given the two points the ellipse passes through, we can substitute in the equation to solve for $a^2$ and $b^2$
Given that the ellipse passes through the points $(4,3)$ and $(6.2)$
We therefore can write the equation of the ellipse as $\;\large\frac{16}{a^2}$$+\large\frac{9}{y^2}$$=1$ and $\;\large\frac{36}{a^2}$$+\large\frac{4}{y^2}$$=1$
Solving the above equations, we get $a^2 = 52, \; b^2 = 13$.
$\Rightarrow$ The equation of the ellipse is $\large\frac{x^2}{52}$$+\large\frac{y^2}{13}$$=1$
answered Apr 3, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App