What is ((x+4)^2)/(25)+((y+1)^2)/(16)=1 ?

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

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((x+4)^2)/(25)+((y+1)^2)/(16)=1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

Rewrite

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

\frac{x ^{2}}{4} + \frac{y ^{2}}{8} = \frac{3}{4}

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{25} = 1

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{9} = 1

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