Question

passing through (2, square root 30 / 3), distance between directrices 24 square root 7 / 7. find the equation of ellipse, center at origin.

Answer 1

have you tried it?

Answer 2

yes but i got stuck up when it comes to distance between directrices..

Answer 3

can you identify the directrices?

Answer 4

sorry but no idea about directrices.. no, i mean its a/e and e is.. a/c. am i right?

Answer 5

e is eccentricity.and yes directrices are at x=a/e and x=-a/e.
so what's the distance between them?

Answer 6

12 square root 7 / 7?

Answer 7

no, i mean dist. btween them is 2a/e .

Answer 8

clear?

Answer 9

i dont understand.. how to get e.. no idea about getting a. im sorry

Answer 10

i'll tell ,first you tell you understand how it is 2a/e?

Answer 11

yes..its the distance between directrices

Answer 12

\[2\frac{a}{e}=24 \frac{\sqrt{7}}{7}\]
\[\frac{a}{e}=12 \frac{\sqrt{7}}{7}\]
\[e= \frac{{7a}}{12\sqrt{7}}\]

Answer 13

yes im following..

Answer 14

also it passes through 2,root(30)/3
so,\[\frac{2^{2}}{a^{2}}+\frac{(\sqrt{30}/3)^{2}}{b^{2}}=1\]

Answer 15

clear till now?

Answer 16

yes

Answer 17

let, A=1/a^2 and B= 1/b^2
so our eq. becomes
\[4A+\frac{30B}{9}=1\]
clear?

Answer 18

yes

Answer 19

also \[e^2 = \frac{49a^2}{144*7}\]
\[e^2 = \frac{7a^2}{144}\]
\[e^2 = \frac{7}{144A}\]
clear?

Answer 20

yes yes

Answer 21

Now...
we have a relation ,you must remember
\[e^2=1-\frac{b^2}{a^2}\]
so
\[e^2=1-\frac{A}{B}\]
equating values of e^2.

\[\frac{7}{144A}=1-\frac{A}{B}\]
\[\frac{7}{144A}=\frac{B-A}{B}\]
\[{7B}=144A(B-A)\]
also we have a relation
\[4A+\frac{30B}{9}=1\]
solving these 2 relation
you'll get A and B.

clear till now??

Answer 22

ill just equate the two relations?

Answer 23

the first relation is the 4A + 30B/9 = 1 and?

Answer 24

that 7B=144A(B-A)

Answer 25

use substitution method.

Answer 26

thank you so much ;))

Answer 27

lifesaver

Answer 28

and wait.. there were two equations in this question.. it was stated in the book

Answer 29

i mean two answers

Answer 30

yes ther are 2 answers.
tell what values of A and B are you getting

Answer 31

you'll get
A=7/88,B=9/44
A=1/12,B=1/5

Answer 32

yes right!!

Answer 33

so the eq. of ellipse is:
\[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\]
\[Ax^2+By^2=1\]

Answer 34

THANK YOU SO MUCH!! :)