Home
Class 11
MATHS
Find the eccentricity coordinates of foc...

Find the eccentricity coordinates of foci length of the latus rectum of the following ellipse: `9x^2+2y^2=225`

Text Solution

Verified by Experts

Given equation of ellipse, `9x^(2)+25y^(2)=225`
`rArr(x^(2))/25+(y^(2))/9=1`
`rArra=5,b=3`
We know that, `b^(2)=a^(2)(1-e^(2))`
`rArr9=25(1-e^(2))`
`rArr9/25=1-e^(2)`
`rArre^(2)=1-9//25`
`thereforee=sqrt(1-9//25)=sqrt((25-9)/25)`
=`sqrt(16/25)=4//5`
Foci=(`pm`ae,0)=(`pm5xx4//5,0)=(pm4,0)`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Long answer|10 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise True/False|8 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Fillers|16 Videos

Similar Questions

Explore conceptually related problems

Find the eccentricity coordinates of foci length of the latus rectum of the following ellipse: 4x^(2)=9y^(2)=1

Find the eccentricity coordinates of foci length of the latus rectum of the following ellipse: 5x^(2)+4y^(2)=1

Find the eccentricity coordinates of foci length of the latus rectum of the following ellipse: 4x^(2)+3y^(2)=1

Find the eccentricity coordinates of foci length of the latus rectum of the following ellipse: 25x^(2)+16y^(2)=1600

Find the eccentricity , co-ordinates of foci, lengths of axes and length of latus-rectum of the ellipse (x^(2) //25) + (y^(2)//9) = 1

Find the (i) lengths of major and minor axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of each of the following ellipses. 3x^(2)+2y^(2)=18

Find the (i) lengths of major and minor axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of each of the following ellipses. x^(2)+4y^(2)=100

Find the (i) lengths of major and minor axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of each of the following ellipses. 9x^(2)+16y^(2)=144

Find the (i) lengths of major and minor axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of each of the following ellipses. 16x^(2)+25y^(2)=400