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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

225 x^{2} + 289 y^{2} = 65025

(2 x^{2} + y^{2})^{2} = (3 - y)^{2}

25 x^{2} + 9 y^{2} = 25

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