What is 6x^2+7y^2=6 ?

The solution to 6x^2+7y^2=6 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(6/7)

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6x^2+7y^2=6

6 x^{2} + 7 y^{2} = 6

(h, k) = (0, 0), a = 1, b = \frac{6}{7}

Solution steps

6 x^{2} + 7 y^{2} = 6

Rewrite

6 x^{2} + 7 y^{2} = 6

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{6}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{6}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1, b = \frac{6}{7}

- 4 y^{2} - 6 y = x^{2}

7 x^{(2)} + 10 y^{(2)} - 56 x + 100 y + 292 = 0

\frac{x ^{2}}{17} + \frac{y ^{2}}{15} = 1

5 x^{2} + 7 y^{2} = 70

\frac{3 x ^{2}}{4} + (\frac{4 y}{4})^{2} = \frac{12}{12}

What is 6x^2+7y^2=6 ?
The solution to 6x^2+7y^2=6 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(6/7)