Question 917854
4x^2 + 9y^2 - 16x + 54y + 96 = 0
4x^2-16x+9y^2+54y = -96
complete the square:
4(x^2-4x+4)+9(y^2+6y+9) = -96+16+81
4(x-2)^2+9(y+3)^2=1
{{{(x-2)^2/(1/4)+(y+3)^2/(1/9)=1}}}
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=center
a) Find the centre:(2,-3)
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b) the two parameters a and b
a^2=1/4
a=1/2
b^2=1/9
b=1/3
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c) the eccentricity=c/a=.37/.5=0.74
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d) the two foci
c^2=a^2-b^2=1/4-1/9=9/36-4/36=5/36
c=√5/6≈0.37
foci:(2±c,-3)=(2±.37,-3)=(2.37,-3)and (1.63,-3)