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

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

2 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

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

3 x^{2} + 2 y^{2} + 2 x - 3 y - 7 = 0

x^{2} + 2 x + 4 y^{2} - 8 y + 1 = 0

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