What is 16-x^2-9y^2=-1 ?

The solution to 16-x^2-9y^2=-1 is Ellipse with (h,k)=(0,0),a=sqrt(17),b=(sqrt(17))/3

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16-x^2-9y^2=-1

16 - x^{2} - 9 y^{2} = - 1

(h, k) = (0, 0), a = 17, b = \frac{17}{3}

Solution steps

16 - x^{2} - 9 y^{2} = - 1

Rewrite

16 - x^{2} - 9 y^{2} = - 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 17 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{17}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 17, b = \frac{17}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 17, b = \frac{17}{3}

y^{2} = 100 - 4 x^{2}

4 x^{2} + y^{2} + 4 x + 8 y + 12 = 0

\frac{( x - 3 ) ^{2}}{18} + \frac{( y + 4 ) ^{2}}{32} = 1

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

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

What is 16-x^2-9y^2=-1 ?
The solution to 16-x^2-9y^2=-1 is Ellipse with (h,k)=(0,0),a=sqrt(17),b=(sqrt(17))/3