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

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

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

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

(h, k) = (5, - 7), a = 5, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( X - 5 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 7), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 7), a = 5, b = 4

6 x^{2} + 10 x + y^{2} = 0

27 x^{2} - 54 x + 48 y^{2} - 192 y - 213 = 0

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

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

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