What is ((x-8)^2}{49}+\frac{(y+5)^2)/9 =1 ?

The solution to ((x-8)^2}{49}+\frac{(y+5)^2)/9 =1 is Ellipse with (h,k)=(8,-5),a=7,b=3

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((x-8)^2}{49}+\frac{(y+5)^2)/9 =1

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{9} = 1

(h, k) = (8, - 5), a = 7, b = 3

Solution steps

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{7 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 5), a = 7, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 5), a = 7, b = 3

\frac{( x - 42 ) ^{2}}{12} + \frac{( y - 20 ) ^{2}}{27} = 1

16 x^{2} + 25 (y + 3)^{2} = 1600

\frac{( x - ( - 1.32 ) ) ^{2}}{3.78} + \frac{y ^{2}}{1.56} = 2

\frac{x ^{2}}{16} - \frac{x}{8} + 9 y^{2} - 18 y + \frac{17}{2} = 0

12 x^{2} + y^{2} = 16

What is ((x-8)^2}{49}+\frac{(y+5)^2)/9 =1 ?
The solution to ((x-8)^2}{49}+\frac{(y+5)^2)/9 =1 is Ellipse with (h,k)=(8,-5),a=7,b=3