What is -x^2-2y^2=-40 ?

The solution to -x^2-2y^2=-40 is Ellipse with (h,k)=(0,0),a=2sqrt(10),b=2sqrt(5)

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-x^2-2y^2=-40

- x^{2} - 2 y^{2} = - 40

(h, k) = (0, 0), a = 210, b = 25

Solution steps

- x^{2} - 2 y^{2} = - 40

Rewrite

- x^{2} - 2 y^{2} = - 40

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 210, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 210, b = 25

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

(\frac{x - 4}{6})^{2} + (\frac{y + 2}{6})^{2} = 1

4 x^{2} + 9 y^{2} = 11

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

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

What is -x^2-2y^2=-40 ?
The solution to -x^2-2y^2=-40 is Ellipse with (h,k)=(0,0),a=2sqrt(10),b=2sqrt(5)