What is ((x-4)^2)/(25)+((y+2)^2)/(64)=1 ?

The solution to ((x-4)^2)/(25)+((y+2)^2)/(64)=1 is Ellipse with (h,k)=(4,-2),a=5,b=8

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((x-4)^2)/(25)+((y+2)^2)/(64)=1

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{64} = 1

(h, k) = (4, - 2), a = 5, b = 8

Solution steps

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{64} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{64} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 5, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 8, a = 5

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{36} = 1

\frac{( x + 4 ) ^{2}}{0.25} + \frac{( y - 8 ) ^{2}}{1} = 1

3 x^{2} + z^{2} = 8 - x^{2} - z^{2}

- \frac{x ^{2}}{1} - \frac{y ^{2}}{4} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

What is ((x-4)^2)/(25)+((y+2)^2)/(64)=1 ?
The solution to ((x-4)^2)/(25)+((y+2)^2)/(64)=1 is Ellipse with (h,k)=(4,-2),a=5,b=8