What is ((X-5)^2)/(25)+((y+7^2)^2)/(16)=1 ?

The solution to ((X-5)^2)/(25)+((y+7^2)^2)/(16)=1 is Ellipse with (h,k)=(5,-49),a=5,b=4

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((X-5)^2)/(25)+((y+7^2)^2)/(16)=1

\frac{( X - 5 ) ^{2}}{25} + \frac{( y + 7 ^{2} ) ^{2}}{16} = 1

(h, k) = (5, - 49), a = 5, b = 4

Solution steps

\frac{( X - 5 ) ^{2}}{25} + \frac{( y + 7 ^{2} ) ^{2}}{16} = 1

Rewrite

\frac{( X - 5 ) ^{2}}{25} + \frac{( y + 7 ^{2} ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( X - 5 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 49 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 49), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 49), a = 5, b = 4

- x^{2} + \frac{2 x}{21} - \frac{17}{21} = y^{2}

\frac{( x - ( - 0.31 ) ) ^{2}}{3.49} + \frac{y ^{2}}{3.71} = 2

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{36} = 1

2 x^{2} + y^{2} - 98 = 0

100 x^{2} + 96 y^{2} - 8840 = 0

What is ((X-5)^2)/(25)+((y+7^2)^2)/(16)=1 ?
The solution to ((X-5)^2)/(25)+((y+7^2)^2)/(16)=1 is Ellipse with (h,k)=(5,-49),a=5,b=4