What is -5x^2-6y^2=1 ?

The solution to -5x^2-6y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/5),b=sqrt(1/6)

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-5x^2-6y^2=1

- 5 x^{2} - 6 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{6}

Solution steps

- 5 x^{2} - 6 y^{2} = 1

Rewrite

- 5 x^{2} - 6 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{6}

\frac{( x + 2 ) ^{2}}{( - 13 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( - 8 ) ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 25

9 x^{2} + 16 y^{2} + 54 x + 64 y + 1 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{4} + \frac{( y + 3 ) ^{2}}{9} = 1

What is -5x^2-6y^2=1 ?
The solution to -5x^2-6y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/5),b=sqrt(1/6)