What is x^2+3(y^2)=84 ?

The solution to x^2+3(y^2)=84 is Ellipse with (h,k)=(0,0),a=2sqrt(21),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+3(y^2)=84

x^{2} + 3 (y^{2}) = 84

(h, k) = (0, 0), a = 221, b = 27

Solution steps

x^{2} + 3 y^{2} = 84

Rewrite

x^{2} + 3 y^{2} = 84

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 21 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 221, b = 27

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 221, b = 27

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

\frac{1}{2} x^{2} + 6 y^{2} - 5 x + \frac{1}{4} y + 8 = 0

x^{2} + \frac{y ^{2}}{36} = 1

α^{2} + 2 β^{2} = 1

What is x^2+3(y^2)=84 ?
The solution to x^2+3(y^2)=84 is Ellipse with (h,k)=(0,0),a=2sqrt(21),b=2sqrt(7)