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

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

Popular >

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

\frac{( ( x + 0 ) ^{2} )}{100} + \frac{( ( y + 0 ) ^{2} )}{49} = 1

2 x^{2} + 3 y^{2} + 9 x + 10 y - 3 = 0

\frac{( x - 9 ) ^{2}}{64} + \frac{( y + 2 ) ^{2}}{25} = 1

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

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