What is ((x+3)^2)/(25)+((y-8)^2)/(16)=1 ?

The solution to ((x+3)^2)/(25)+((y-8)^2)/(16)=1 is Ellipse with (h,k)=(-3,8),a=5,b=4

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((x+3)^2)/(25)+((y-8)^2)/(16)=1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

(h, k) = (- 3, 8), a = 5, b = 4

Solution steps

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

Rewrite

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{5 ^{2}} + \frac{( y - 8 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 8), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 8), a = 5, b = 4

16 x^{2} + 9 y^{2} - 36 y = 108

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

x^{(2)} + 4 y^{(2)} + 2 x - 12 y + 6 = 0

2 x - x^{2} - 4 y^{2} - 16 y - 1 > 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{64} = 1

What is ((x+3)^2)/(25)+((y-8)^2)/(16)=1 ?
The solution to ((x+3)^2)/(25)+((y-8)^2)/(16)=1 is Ellipse with (h,k)=(-3,8),a=5,b=4