What is x^2+6x+(5y+6)^2-2(5y+6)+10=4 ?

The solution to x^2+6x+(5y+6)^2-2(5y+6)+10=4 is Ellipse with (h,k)=(-3,-1),a=2,b= 2/5

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x^2+6x+(5y+6)^2-2(5y+6)+10=4

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

(h, k) = (- 3, - 1), a = 2, b = \frac{2}{5}

Solution steps

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

Rewrite

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 1), a = 2, b = \frac{2}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 1), a = 2, b = \frac{2}{5}

25 y^{2} + 36 (x - 8)^{2} = 900

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

4 x^{2} + 3 y^{2} - 32 x - 18 y + 43 = 0

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

100 x^{2} + 64 y^{2} < 1600

What is x^2+6x+(5y+6)^2-2(5y+6)+10=4 ?
The solution to x^2+6x+(5y+6)^2-2(5y+6)+10=4 is Ellipse with (h,k)=(-3,-1),a=2,b= 2/5