What is (x^2)/2+(y^2)/7 =1 ?

The solution to (x^2)/2+(y^2)/7 =1 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=sqrt(7)

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(x^2)/2+(y^2)/7 =1

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

(h, k) = (0, 0), a = 2, b = 7

Solution steps

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

Rewrite

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 7, a = 2

2 (x^{2} + 3 x + 2.25) + y (3 y - 1 + 1) = - 4 + 4.5 + 1

9 x^{2} + 26 y^{2} = 60

8 x^{2} + 9 y^{2} - 16 x - 54 y + 17 = 0

x^{2} + 3 y^{2} = 112

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

What is (x^2)/2+(y^2)/7 =1 ?
The solution to (x^2)/2+(y^2)/7 =1 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=sqrt(7)