What is ((x^2))/(16)+((y^2))/(25)=1 ?

The solution to ((x^2))/(16)+((y^2))/(25)=1 is Ellipse with (h,k)=(0,0),a=4,b=5

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((x^2))/(16)+((y^2))/(25)=1

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{25} = 1

(h, k) = (0, 0), a = 4, b = 5

Solution steps

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

Rewrite

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 4

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

\frac{( x - 8 ) ^{2}}{12} + \frac{( y + 1 ) ^{2}}{16} = 1

16 x^{2} + 25 y^{2} + 160 x + 200 y + 400 = 0

36 x^{2} + 5 y^{2} + 216 x - 60 y + 324 = 0

x^{2} + 4 y^{2} + 8 x + 9 y - 9 = 0

What is ((x^2))/(16)+((y^2))/(25)=1 ?
The solution to ((x^2))/(16)+((y^2))/(25)=1 is Ellipse with (h,k)=(0,0),a=4,b=5