What is 2x^2+y^2+4x-6y-12=0 ?

The solution to 2x^2+y^2+4x-6y-12=0 is Ellipse with (h,k)=(-1,3),a=sqrt(23/2),b=sqrt(23)

Popular >

2x^2+y^2+4x-6y-12=0

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

(h, k) = (- 1, 3), a = \frac{23}{2}, b = 23

Solution steps

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

Rewrite

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{23}{2} ) ^{2}} + \frac{( y - 3 ) ^{2}}{( 23 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = \frac{23}{2}, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), b = 23, a = \frac{23}{2}

(\frac{X}{16})^{2} + \frac{( Y + 1 ) ^{2}}{4} - 1 = 0

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

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

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

What is 2x^2+y^2+4x-6y-12=0 ?
The solution to 2x^2+y^2+4x-6y-12=0 is Ellipse with (h,k)=(-1,3),a=sqrt(23/2),b=sqrt(23)