ELLIPSE

[r267747]

HERE IS THE COMPLEX QUESIONS EVEN WHICH MY TEACHER ALSO NOT UNDERSTAND SO PLEASE SOLVE THIS QUESTION
QUES1) Find the =n of the ellipse reffered to its centre as origin and axes along the co-ordinate axes, whose minor axis is equalto the distance b/t the foci and whose latus rectum is 10.
ques2) please give me a hint for this
Find the -n of the set of all points whose distances from (0,4) are 2/3 of their distances from the line y=9.

 

[daon]

Please use proper english when posting.

"=n", "reffered to its centre as origin and axes along the co-ordinate axes", " whose minor axis is equalto the distance b/t the foci "

I think I know what you meant, but please clarify.

Also, why in the world would your teacher assign something he/she does not understand?

Here is the equation for an ellipse centered at the origin:

\(\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

If a>b then the focus of an ellpise centered at the origin lies at:

\(\displaystyle \pm x_f, x_f=\sqrt{a^2-b^2}\)

Hence the distance between the foci is:

\(\displaystyle d = 2x_f = 2\sqrt{a^2-b^2}\)

The formula for the latus rectum of an ellipse, centered at the origin, is given by the four points (from which you may determine the lengths):

\(\displaystyle (x,y) = (\pm x_f, \pm \frac{b^2}{a})\)

I will leave the derivation to you, however. It is not difficult and is a good, basic, exercise in algebra.