What is (x^2}{10}+\frac{y^2)/2 =1 ?

The solution to (x^2}{10}+\frac{y^2)/2 =1 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=sqrt(2)

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

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

(h, k) = (0, 0), a = 10, b = 2

Solution steps

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

Rewrite

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 2

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

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

\frac{x ^{2}}{2 0 ^{2}} + \frac{y ^{2}}{1 5 ^{2}} = 1

25 x^{2} + 16 y^{2} - 100 x - 300 = 0

4 x^{2} + 24 x + 25 y^{2} - 300 y + 836 = 0

What is (x^2}{10}+\frac{y^2)/2 =1 ?
The solution to (x^2}{10}+\frac{y^2)/2 =1 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=sqrt(2)