What is ((X-7)^2)/(25)+((Y-3)^2)/(16)=1 ?

The solution to ((X-7)^2)/(25)+((Y-3)^2)/(16)=1 is Ellipse with (h,k)=(7,3),a=5,b=4

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((X-7)^2)/(25)+((Y-3)^2)/(16)=1

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 1

(h, k) = (7, 3), a = 5, b = 4

Solution steps

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 1

Rewrite

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( X - 7 ) ^{2}}{5 ^{2}} + \frac{( Y - 3 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, 3), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, 3), a = 5, b = 4

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

5 x^{2} + 10 y^{2} + 125 x + 125 y + 44 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{9} = 1

What is ((X-7)^2)/(25)+((Y-3)^2)/(16)=1 ?
The solution to ((X-7)^2)/(25)+((Y-3)^2)/(16)=1 is Ellipse with (h,k)=(7,3),a=5,b=4