What is 9x^2+5y^2+18x-10y-31=0 ?

The solution to 9x^2+5y^2+18x-10y-31=0 is Ellipse with (h,k)=(-1,1),a=sqrt(5),b=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9x^2+5y^2+18x-10y-31=0

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

(h, k) = (- 1, 1), a = 5, b = 3

Solution steps

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

Rewrite

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 5, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 3, a = 5

\frac{( x - 3 ) ^{2}}{25} + \frac{y ^{2}}{9} = 1

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

4 x^{2} - 16 x + y^{2} + 2 y = - 1

4 x^{2} + 9 y^{2} = 4

2 x^{2} + 3 y^{2} = 1

What is 9x^2+5y^2+18x-10y-31=0 ?
The solution to 9x^2+5y^2+18x-10y-31=0 is Ellipse with (h,k)=(-1,1),a=sqrt(5),b=3