Question

show that 4x^2+9y^2=36 represent an ellipse
find its directrix and eccentricity

Answer 1

ok so i show that it is an ellipse by dividing throughout by 36 and simplifying to get \[\frac{ x^2 }{ 9 }+\frac{ y^2 }{ 4 }=1\]

Answer 2

how do i find the directrix and eccentricity?

Answer 3

@ganeshie8

Answer 4

Hey!

Answer 5

From the standard form, can you figure out the values of \(a\) and \(b\) ?

Answer 6

Once you have \(a\) and \(b\), you may use below definition to find the value of eccentricity.
http://www.mathopenref.com/ellipseeccentricity.html

Answer 7

An ellipse does not have a directrix.

Answer 8

yea it does ..well that what was ask for the question

Answer 9

c^2=9-4
c=sq.rt 5
so the focus is (sq.rt5,0)
for the eccentricity i got c/a which gives (sq.rt 5)/3

for the directrix i got x=a^2/c
which gives 9/sq.rt 5

is this correct

Answer 10

@ganeshie8

Answer 11

yes, that looks good

Answer 12

ok thanks