What is ((x-5)^2)/(47)+((y+3)^2)/(30)=1 ?

The solution to ((x-5)^2)/(47)+((y+3)^2)/(30)=1 is Ellipse with (h,k)=(5,-3),a=sqrt(47),b=sqrt(30)

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((x-5)^2)/(47)+((y+3)^2)/(30)=1

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

(h, k) = (5, - 3), a = 47, b = 30

Solution steps

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 47 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 30 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 3), a = 47, b = 30

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = 47, b = 30

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

8 x^{2} + 16 y^{2} = 1

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

4 x^{2} + 9 y^{2} \leq 36

What is ((x-5)^2)/(47)+((y+3)^2)/(30)=1 ?
The solution to ((x-5)^2)/(47)+((y+3)^2)/(30)=1 is Ellipse with (h,k)=(5,-3),a=sqrt(47),b=sqrt(30)