Write the formula you will use to write the equation of this ellipse. Write the standard form equation of the ellipse.

Question

 

Formula for an ellipes not centered at the  origin is : ( x - h) ^2 a^2 + ( y - v)^2 /b^2 = 1

Answer 1

Calculate the center of the ellipse:

Midpoint of the (0,0)(-6,0)

(h,k) =((0+(-6))/2,(0+0)/2)=(-3,0)

Calculate the length of the major axis,

2a=sqrt((5-(-5))^2+(-3-(-3))^2)

     =10

a=5

Calculate the length of the minor axis,

2b=sqrt((0-(-6))^2+(0-0)^2)

     =6

b=3

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(x-h)^2/b^2+(y-k)^2/a^2=1

(x-(-3))^2/3^2+(y-0)^2/5^2=1

(x+3)^2/9+y^2/25 =1