What is 5x^2+2y^2=50 ?

The solution to 5x^2+2y^2=50 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=5

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5x^2+2y^2=50

5 x^{2} + 2 y^{2} = 50

(h, k) = (0, 0), a = 10, b = 5

Solution steps

5 x^{2} + 2 y^{2} = 50

Rewrite

5 x^{2} + 2 y^{2} = 50

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 10

4 x^{2} + 9 y^{2} - 16 x + 36 y + 16 = 0

5 x^{2} + 2 y^{2} = 10

3 x^{2} + 6 y^{2} - 4 x + 6 y - 3 \geq 0

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

What is 5x^2+2y^2=50 ?
The solution to 5x^2+2y^2=50 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=5