What is 18x^2+4y^2+4y-72x+37=0 ?

The solution to 18x^2+4y^2+4y-72x+37=0 is Ellipse with (h,k)=(2,-1/2),a=sqrt(2),b=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

18x^2+4y^2+4y-72x+37=0

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

(h, k) = (2, - \frac{1}{2}), a = 2, b = 3

Solution steps

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

Rewrite

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - \frac{1}{2}), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{1}{2}), b = 3, a = 2

x^{2} - 2 x + 2 y^{2} - 8 y + 7 = 0

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

9 x^{2} + 4 y^{2} - 36 x + 24 y + 36 = 0

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

y^{2} = 4 - 4 x^{2}

What is 18x^2+4y^2+4y-72x+37=0 ?
The solution to 18x^2+4y^2+4y-72x+37=0 is Ellipse with (h,k)=(2,-1/2),a=sqrt(2),b=3