What is 4x^2-24x+36y^2-360y+864=0 ?

The solution to 4x^2-24x+36y^2-360y+864=0 is Ellipse with (h,k)=(3,5),a=3sqrt(2),b=sqrt(2)

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4x^2-24x+36y^2-360y+864=0

4 x^{2} - 24 x + 36 y^{2} - 360 y + 864 = 0

(h, k) = (3, 5), a = 32, b = 2

Solution steps

4 x^{2} - 24 x + 36 y^{2} - 360 y + 864 = 0

Rewrite

4 x^{2} - 24 x + 36 y^{2} - 360 y + 864 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 3 2 ) ^{2}} + \frac{( y - 5 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 5), a = 32, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 5), a = 32, b = 2

3 (x - 1)^{2} + (y - 3)^{2} = 27

4 x^{2} + y^{2} + 4 x + 2 y + 1 = 0

\frac{( x - 1 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{1}{x + y i} + \frac{1}{x - y i} < - 1

6 x^{2} + 9 y^{2} = 54

What is 4x^2-24x+36y^2-360y+864=0 ?
The solution to 4x^2-24x+36y^2-360y+864=0 is Ellipse with (h,k)=(3,5),a=3sqrt(2),b=sqrt(2)