What is 5x^2+9y^2-20x-18y-16=0 ?

The solution to 5x^2+9y^2-20x-18y-16=0 is Ellipse with (h,k)=(2,1),a=3,b=sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5x^2+9y^2-20x-18y-16=0

5 x^{2} + 9 y^{2} - 20 x - 18 y - 16 = 0

(h, k) = (2, 1), a = 3, b = 5

Solution steps

5 x^{2} + 9 y^{2} - 20 x - 18 y - 16 = 0

Rewrite

5 x^{2} + 9 y^{2} - 20 x - 18 y - 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 3, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 3, b = 5

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

\frac{( x - 0 ) ^{2}}{20} + \frac{( y - 0 ) ^{2}}{36} = 1

2 x^{2} + 4 y^{2} = 200

3 x^{2} + 4 y^{2} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1

What is 5x^2+9y^2-20x-18y-16=0 ?
The solution to 5x^2+9y^2-20x-18y-16=0 is Ellipse with (h,k)=(2,1),a=3,b=sqrt(5)