What is 7x^2+2y^2-14=0 ?

The solution to 7x^2+2y^2-14=0 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=sqrt(7)

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7x^2+2y^2-14=0

7 x^{2} + 2 y^{2} - 14 = 0

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

Solution steps

7 x^{2} + 2 y^{2} - 14 = 0

Rewrite

7 x^{2} + 2 y^{2} - 14 = 0

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

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} = 1

9 x^{2} + 49 y^{2} + 108 x - 196 y + 79 = 0

- 2 y^{2} - x^{2} + y + 79 = 0

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

4 x^{2} + y^{2} = 800

What is 7x^2+2y^2-14=0 ?
The solution to 7x^2+2y^2-14=0 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=sqrt(7)