What is 2x^2-8x+y^2+6y+15=0 ?

The solution to 2x^2-8x+y^2+6y+15=0 is Ellipse with (h,k)=(2,-3),a=1,b=sqrt(2)

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2x^2-8x+y^2+6y+15=0

2 x^{2} - 8 x + y^{2} + 6 y + 15 = 0

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

Solution steps

2 x^{2} - 8 x + y^{2} + 6 y + 15 = 0

Rewrite

2 x^{2} - 8 x + y^{2} + 6 y + 15 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

What is 2x^2-8x+y^2+6y+15=0 ?
The solution to 2x^2-8x+y^2+6y+15=0 is Ellipse with (h,k)=(2,-3),a=1,b=sqrt(2)