What is ((x+3)^2)/(21)+((y-6)^2)/(25)=1 ?

The solution to ((x+3)^2)/(21)+((y-6)^2)/(25)=1 is Ellipse with (h,k)=(-3,6),a=sqrt(21),b=5

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((x+3)^2)/(21)+((y-6)^2)/(25)=1

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

(h, k) = (- 3, 6), a = 21, b = 5

Solution steps

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 21 ) ^{2}} + \frac{( y - 6 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 6), a = 21, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 6), b = 5, a = 21

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

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

x^{(2)} + 4 x + 4 y^{(2)} - 6 y + 9 = 3

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

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

What is ((x+3)^2)/(21)+((y-6)^2)/(25)=1 ?
The solution to ((x+3)^2)/(21)+((y-6)^2)/(25)=1 is Ellipse with (h,k)=(-3,6),a=sqrt(21),b=5