What is x^2+7y^2=12 ?

The solution to x^2+7y^2=12 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=(2sqrt(3))/(sqrt(7))

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x^2+7y^2=12

x^{2} + 7 y^{2} = 12

(h, k) = (0, 0), a = 23, b = \frac{2 3}{7}

Solution steps

x^{2} + 7 y^{2} = 12

Rewrite

x^{2} + 7 y^{2} = 12

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2 3}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23, b = \frac{2 3}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 23, b = \frac{2 3}{7}

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} < 1

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{\frac{9}{25}} = 1

y = 4 - \frac{x ^{2}}{4 y}

What is x^2+7y^2=12 ?
The solution to x^2+7y^2=12 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=(2sqrt(3))/(sqrt(7))