What is ((x+6)^2)/(25)+((y+1)^2)/(16)=1 ?

The solution to ((x+6)^2)/(25)+((y+1)^2)/(16)=1 is Ellipse with (h,k)=(-6,-1),a=5,b=4

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((x+6)^2)/(25)+((y+1)^2)/(16)=1

\frac{( x + 6 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

(h, k) = (- 6, - 1), a = 5, b = 4

Solution steps

\frac{( x + 6 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

Rewrite

\frac{( x + 6 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, - 1), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, - 1), a = 5, b = 4

2 x^{2} - 5 x + 3 y^{2} - 4 y = 1

5 x^{2} + 10 y^{2} = 5

3 x^{2} + 3 y^{2} + 36 y = 0

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 7 ) ^{2}}{81} = 1

\frac{( x + 1 ) ^{2}}{100} + \frac{( y - 6 ) ^{2}}{64} = 1

What is ((x+6)^2)/(25)+((y+1)^2)/(16)=1 ?
The solution to ((x+6)^2)/(25)+((y+1)^2)/(16)=1 is Ellipse with (h,k)=(-6,-1),a=5,b=4