What is 4x^2+9y^2-8x+36y-104=0 ?

The solution to 4x^2+9y^2-8x+36y-104=0 is Ellipse with (h,k)=(1,-2),a=6,b=4

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4x^2+9y^2-8x+36y-104=0

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

(h, k) = (1, - 2), a = 6, b = 4

Solution steps

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

Rewrite

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 6, b = 4

\frac{( y - 3 ) ^{2}}{9} + \frac{( x - 2 ) ^{2}}{2} = 1

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

25 y^{2} + 16 x^{2} + 50 y - 64 x - 311 = 0

25 x^{2} + 100 y^{2} = 400

4 x^{2} + 9 y^{2} - 8 x + 3 y + 4 = 0

What is 4x^2+9y^2-8x+36y-104=0 ?
The solution to 4x^2+9y^2-8x+36y-104=0 is Ellipse with (h,k)=(1,-2),a=6,b=4