What is (x^2)/(16)+((y+4)^2)/(81)=1 ?

The solution to (x^2)/(16)+((y+4)^2)/(81)=1 is Ellipse with (h,k)=(0,-4),a=4,b=9

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(x^2)/(16)+((y+4)^2)/(81)=1

\frac{x ^{2}}{16} + \frac{( y + 4 ) ^{2}}{81} = 1

(h, k) = (0, - 4), a = 4, b = 9

Solution steps

\frac{x ^{2}}{16} + \frac{( y + 4 ) ^{2}}{81} = 1

Rewrite

\frac{x ^{2}}{16} + \frac{( y + 4 ) ^{2}}{81} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 4), a = 4, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 4), b = 9, a = 4

16 - 4 x^{2} - y^{2} \geq 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{4} = 1

16 x^{2} + 25 y^{2} - 32 x + 50 y + 16 = 0

4 x^{2} + 16 y^{2} - 64 = 0

\frac{x ^{2}}{12} + \frac{y ^{2}}{80} = 1

What is (x^2)/(16)+((y+4)^2)/(81)=1 ?
The solution to (x^2)/(16)+((y+4)^2)/(81)=1 is Ellipse with (h,k)=(0,-4),a=4,b=9