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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}

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