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

The center 4x^2+9y^2-8x-36y+4=0 is (1,2)

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

center

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

(1, 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

And the center is:

(1, 2)

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{25} = 1

2 x^{2} + 2 y^{2} + 4 y = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{7} = 1

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

\frac{x ^{2}}{9} + y^{2} = 1

What is the center 4x^2+9y^2-8x-36y+4=0 ?
The center 4x^2+9y^2-8x-36y+4=0 is (1,2)