What is (x^2)/9+(y^2)/4 =y+6 ?

The solution to (x^2)/9+(y^2)/4 =y+6 is Ellipse with (h,k)=(0,2),a=3sqrt(7),b=2sqrt(7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x^2)/9+(y^2)/4 =y+6

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

(h, k) = (0, 2), a = 37, b = 27

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 7 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 37, b = 27

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 37, b = 27

2 (x^{2} + 3 x) + y (3 y - 1) = - 4

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

25 \cdot x^{2} + 9 \cdot y^{2} = 225

2 x^{2} + 5 y^{2} + 3 x + 5 y - 6 = 0

\frac{( x - 3 ) ^{2}}{16} + (\frac{y + 2}{9})^{2} = 1

What is (x^2)/9+(y^2)/4 =y+6 ?
The solution to (x^2)/9+(y^2)/4 =y+6 is Ellipse with (h,k)=(0,2),a=3sqrt(7),b=2sqrt(7)