What is 16x^2+36y^2-96x+36y+9=0 ?

The solution to 16x^2+36y^2-96x+36y+9=0 is Ellipse with (h,k)=(3,-1/2),a=3,b=2

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16x^2+36y^2-96x+36y+9=0

16 x^{2} + 36 y^{2} - 96 x + 36 y + 9 = 0

(h, k) = (3, - \frac{1}{2}), a = 3, b = 2

Solution steps

16 x^{2} + 36 y^{2} - 96 x + 36 y + 9 = 0

Rewrite

16 x^{2} + 36 y^{2} - 96 x + 36 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - \frac{1}{2}), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - \frac{1}{2}), a = 3, b = 2

\frac{x ^{2}}{144} + \frac{y ^{2}}{16} = 1

(2 x - 2)^{2} + (3 y - 6)^{2} = 36

\frac{x ^{2}}{12} + \frac{y ^{2}}{16} = 1

\frac{3}{2} u^{2} + \frac{1}{2} v^{2} = 4

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

What is 16x^2+36y^2-96x+36y+9=0 ?
The solution to 16x^2+36y^2-96x+36y+9=0 is Ellipse with (h,k)=(3,-1/2),a=3,b=2