What is 4x^2+9y^2-24x+18y+9=0 ?

The solution to 4x^2+9y^2-24x+18y+9=0 is Ellipse with (h,k)=(3,-1),a=3,b=2

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4x^2+9y^2-24x+18y+9=0

4 x^{2} + 9 y^{2} - 24 x + 18 y + 9 = 0

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

Solution steps

4 x^{2} + 9 y^{2} - 24 x + 18 y + 9 = 0

Rewrite

4 x^{2} + 9 y^{2} - 24 x + 18 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

3 x^{2} + 3 y^{2} - 30 y = 0

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

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

x^{2} + 4 y^{2} + 4 x + 32 y - 64 = 0

What is 4x^2+9y^2-24x+18y+9=0 ?
The solution to 4x^2+9y^2-24x+18y+9=0 is Ellipse with (h,k)=(3,-1),a=3,b=2