What is 2x^2-4x+y^2-6y=9 ?

The solution to 2x^2-4x+y^2-6y=9 is Ellipse with (h,k)=(1,3),a=sqrt(10),b=2sqrt(5)

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2x^2-4x+y^2-6y=9

2 x^{2} - 4 x + y^{2} - 6 y = 9

(h, k) = (1, 3), a = 10, b = 25

Solution steps

2 x^{2} - 4 x + y^{2} - 6 y = 9

Rewrite

2 x^{2} - 4 x + y^{2} - 6 y = 9

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 3), a = 10, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 3), b = 25, a = 10

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

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

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

9 x^{2} + y^{2} + 90 x - 4 y + 193 = 0

\frac{x ^{2}}{16} + \frac{x}{2} + \frac{y ^{2}}{4} + y + 1 = 0

What is 2x^2-4x+y^2-6y=9 ?
The solution to 2x^2-4x+y^2-6y=9 is Ellipse with (h,k)=(1,3),a=sqrt(10),b=2sqrt(5)