10 Write the equation of the ellipse in standard form and id

10. Write the equation of the ellipse in standard form, and identify the end points of the major and minor axes as well as the foci.

Write the equation of the ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 16z2 +4y-640 Equation in standard form: End points of major axis: (, Preview End points of minor axis: ( ,),(,) Foci are at: Preview Preview Preview Preview

Solution

16x^2 + 4y^2 - 64 = 0

putting the equation in standard form

16x^2 + 4y^2 = 64

dividing both sides by 64

x^2 / 4 + y^2 / 16 = 1

b) major axis is 2a = 2* 4 = 8

hence, end points of major axis are

( 0,4 ) , (0,-4)  

minor axis is 2*2 = 4

endpoints of minor axis are

(-2,0) and (2,0)

c^2 = a^2 - b^2

c = sqrt ( 16 - 4 ) = 2 sqrt 3

hence, foci are

( 0 , 2sqrt 3 ) , ( 0 , - 2 sqrt 3 )