What is 9x^2-54x+4y^2=-45 ?

The solution to 9x^2-54x+4y^2=-45 is Ellipse with (h,k)=(3,0),a=2,b=3

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9x^2-54x+4y^2=-45

9 x^{2} - 54 x + 4 y^{2} = - 45

(h, k) = (3, 0), a = 2, b = 3

Solution steps

9 x^{2} - 54 x + 4 y^{2} = - 45

Rewrite

9 x^{2} - 54 x + 4 y^{2} = - 45

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 0), b = 3, a = 2

x^{2} + 3 y^{2} + x - 2 y - 1 = 0

(\frac{x + 7}{16})^{2} + \frac{( y + 5 ) ^{2}}{16} = 1

3 x^{2} + 2 y^{2} + 12 x - 8 y - 16 = 0

16 x^{2} + 25 y^{2} = 1.6

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

What is 9x^2-54x+4y^2=-45 ?
The solution to 9x^2-54x+4y^2=-45 is Ellipse with (h,k)=(3,0),a=2,b=3