What is 3(3x^2+9y^2-2x-36)=-82 ?

The solution to 3(3x^2+9y^2-2x-36)=-82 is Ellipse with (h,k)=(1/3 ,0),a=sqrt(3),b=1

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3(3x^2+9y^2-2x-36)=-82

3 (3 x^{2} + 9 y^{2} - 2 x - 36) = - 82

(h, k) = (\frac{1}{3}, 0), a = 3, b = 1

Solution steps

3 (3 x^{2} + 9 y^{2} - 2 x - 36) = - 82

Rewrite

3 (3 x^{2} + 9 y^{2} - 2 x - 36) = - 82

in the form of the standard ellipse equation

\frac{( x - \frac{1}{3} ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{3}, 0), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{3}, 0), a = 3, b = 1

h (x) h (x) = - 5 x^{2} + 10 x + 15

9 x^{2} + y^{2} - 81 = 0

\frac{x ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

16 x^{2} + 80 y^{2} = 1280

\frac{5 x ^{2} + y ^{2} - 15 x + 8 y - 11}{4} = 0

What is 3(3x^2+9y^2-2x-36)=-82 ?
The solution to 3(3x^2+9y^2-2x-36)=-82 is Ellipse with (h,k)=(1/3 ,0),a=sqrt(3),b=1