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sketch and discuss the ellipse:x^2+9y^2+4x-18y-23=0

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Posted in Calculus, asked by joseph, 6 years ago. 1903 hits.

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given equation,x^2+9y^2+4x-18y-23=0we can rearrange the given equation,x^2+4x+9y^2-18y=23

                                                   x^2+4x+4+9(y^2-2y+1)=23+4+9

                                                  (x+2)^2+9(y-1)^2=36

                                                  1/36(x+2)^2+9/36(y-1)^2=1

                                                  1/6^2(x+2)^2+1/2^2(y-1)^2=1

equation of the eclipse is,(x-h)^2/a^2+(y-k)^2/b^2=1

 center=(h,k)=(-2,1)

  vertices=(a,0),(-a,0)=(6,0),(-6,0)

Y intercepts=(0,b),(0,-b)=(0,2),(0,-2)

length of major axis=2a=2*6=12

length of minor axis=2b=2*2=4

c^2=a^2-b^2=6^2-2^2=36-4=32=>c=4root2

foci=(c,0),(-c,0)=(4root2,0),(-4root2,0)

 

 

Venkat Nagendra Thati
Venkat Nagendra Thati - 6 years ago
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