What is 2x^2+y^2-8x+4y+2=0 ?

The solution to 2x^2+y^2-8x+4y+2=0 is Ellipse with (h,k)=(2,-2),a=sqrt(5),b=sqrt(10)

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2x^2+y^2-8x+4y+2=0

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

(h, k) = (2, - 2), a = 5, b = 10

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 2), a = 5, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 2), b = 10, a = 5

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

4 - x^{2} - 4 y^{2} \geq 0

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{45} = 1

\frac{( x - 3 ) ^{2} + y ^{2}}{( x + 3 ) ^{2} + y ^{2}} \geq 4

What is 2x^2+y^2-8x+4y+2=0 ?
The solution to 2x^2+y^2-8x+4y+2=0 is Ellipse with (h,k)=(2,-2),a=sqrt(5),b=sqrt(10)