What is (x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9 ?

The solution to (x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9 is Ellipse with (h,k)=(0,-4),a=2,b=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

(h, k) = (0, - 4), a = 2, b = 2

Solution steps

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

Rewrite

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 4), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 4), b = 2, a = 2

What is (x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9 ?
The solution to (x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9 is Ellipse with (h,k)=(0,-4),a=2,b=2