What is the center 4x^2+36y^2-24x-288y+611=0 ?

The center 4x^2+36y^2-24x-288y+611=0 is (3,4)

Popular >

center 4x^2+36y^2-24x-288y+611=0

center

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

(3, 4)

Solution steps

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

Rewrite

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - 4 ) ^{2}}{( \frac{1}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

And the center is:

(3, 4)

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

25 x^{2} + 144 y^{2} = 900

x^{2} + 4 \cdot y^{2} - 4 \cdot y = 0

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

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

What is the center 4x^2+36y^2-24x-288y+611=0 ?
The center 4x^2+36y^2-24x-288y+611=0 is (3,4)