What is ((x^2+6x+9))/(49)+((y^2-2y+1))/(45)=1 ?

The solution to ((x^2+6x+9))/(49)+((y^2-2y+1))/(45)=1 is Ellipse with (h,k)=(-3,1),a=7,b=3sqrt(5)

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((x^2+6x+9))/(49)+((y^2-2y+1))/(45)=1

\frac{( x ^{2} + 6 x + 9 )}{49} + \frac{( y ^{2} - 2 y + 1 )}{45} = 1

(h, k) = (- 3, 1), a = 7, b = 35

Solution steps

\frac{x ^{2} + 6 x + 9}{49} + \frac{y ^{2} - 2 y + 1}{45} = 1

Rewrite

\frac{x ^{2} + 6 x + 9}{49} + \frac{y ^{2} - 2 y + 1}{45} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 7, b = 35

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), a = 7, b = 35

\frac{( y - 5 ) ^{2}}{16} + \frac{( x - 3 ) ^{2}}{4} = 1

x^{2} + 4 y^{2} + 4 x = 0

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

2 x^{2} + 9 y^{2} = 1

16 - 4 x^{(2)} - y^{(2)} \geq 0

What is ((x^2+6x+9))/(49)+((y^2-2y+1))/(45)=1 ?
The solution to ((x^2+6x+9))/(49)+((y^2-2y+1))/(45)=1 is Ellipse with (h,k)=(-3,1),a=7,b=3sqrt(5)