What is 5x^2+9y^2-80x+54y+221=0 ?

The solution to 5x^2+9y^2-80x+54y+221=0 is Ellipse with (h,k)=(8,-3),a=6,b=2sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

5x^2+9y^2-80x+54y+221=0

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

(h, k) = (8, - 3), a = 6, b = 25

Solution steps

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

Rewrite

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 3), a = 6, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 3), a = 6, b = 25

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

49 x^{2} + 25 y^{2} - 1225 = 0

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

2 x^{2} + 5 y^{2} - 4 x + y - 6 = 0

\frac{( x - 2.63 ) ^{2}}{1.34} + \frac{y ^{2}}{3.22} - 1 = 1

What is 5x^2+9y^2-80x+54y+221=0 ?
The solution to 5x^2+9y^2-80x+54y+221=0 is Ellipse with (h,k)=(8,-3),a=6,b=2sqrt(5)