What is (y^2}{10}+\frac{x^2)/6 =1 ?

The solution to (y^2}{10}+\frac{x^2)/6 =1 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(10)

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(y^2}{10}+\frac{x^2)/6 =1

\frac{y ^{2}}{10} + \frac{x ^{2}}{6} = 1

(h, k) = (0, 0), a = 6, b = 10

Solution steps

\frac{y ^{2}}{10} + \frac{x ^{2}}{6} = 1

Rewrite

\frac{y ^{2}}{10} + \frac{x ^{2}}{6} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 6

x^{2} - 8 x + 2 y^{2} + 8 y = 20

x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

169 x^{2} + 25 y^{2} = 4225

3 x^{2} + 4 y^{2} + 28 x - 16 y + 48 = 0

6 x^{2} + y^{2} - 12 x + 2 y = 1

What is (y^2}{10}+\frac{x^2)/6 =1 ?
The solution to (y^2}{10}+\frac{x^2)/6 =1 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(10)