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

The solution to 4x^2+9y^2-8x+36y+4=0 is Ellipse with (h,k)=(1,-2),a=3,b=2

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

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

(h, k) = (1, - 2), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (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) = (1, - 2), a = 3, b = 2

- 5 x^{2} - 6 y^{2} = 1

\frac{( x + 2 ) ^{2}}{( - 13 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( - 8 ) ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 25

9 x^{2} + 16 y^{2} + 54 x + 64 y + 1 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{16} = 1

What is 4x^2+9y^2-8x+36y+4=0 ?
The solution to 4x^2+9y^2-8x+36y+4=0 is Ellipse with (h,k)=(1,-2),a=3,b=2