What is (x^2)/(-12)+(y^2)/(-12-16)=1 ?

The solution to (x^2)/(-12)+(y^2)/(-12-16)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(3)i,b=2sqrt(7)i

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(x^2)/(-12)+(y^2)/(-12-16)=1

\frac{x ^{2}}{- 12} + \frac{y ^{2}}{- 12 - 16} = 1

(h, k) = (0, 0), a = 23 i, b = 27 i

Solution steps

\frac{x ^{2}}{- 12} + \frac{y ^{2}}{- 12 - 16} = 1

Rewrite

\frac{x ^{2}}{- 12} + \frac{y ^{2}}{- 12 - 16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23 i, b = 27 i

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 23 i, b = 27 i

\frac{( X + 2 ) ^{2}}{9} + \frac{( Y - 1 ) ^{2}}{16} = 1

\frac{x}{x ^{2} + y ^{2}} \leq \frac{1}{2}

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

a^{2} + 2 b^{2} = 1

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

What is (x^2)/(-12)+(y^2)/(-12-16)=1 ?
The solution to (x^2)/(-12)+(y^2)/(-12-16)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(3)i,b=2sqrt(7)i