What is ((x+2)^2)/(4^2)+((y-1)^2)/(5^2)=1 ?

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

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((x+2)^2)/(4^2)+((y-1)^2)/(5^2)=1

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

(h, k) = (- 2, 1), a = 4, b = 5

Solution steps

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 5, a = 4

x^{2} + y^{2} = - y^{2} + 4

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

\frac{( x + 9 ) ^{2}}{2} + \frac{y ^{2}}{3} = 1

\frac{x ^{2}}{625} + \frac{y ^{2}}{400} = 1

14 x^{2} + 8 y^{2} = 112

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