What is 4=4x^2+y^2+1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4=4x^2+y^2+1

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

(h, k) = (0, 0), a = \frac{3}{2}, b = 3

Solution steps

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

Rewrite

4 - 4 x^{2} - y^{2} - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{3}{2}, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = \frac{3}{2}

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{x ^{2}}{1} + \frac{y ^{2}}{15} = 1

9 x^{2} + 16 y^{2} + 72 x = 0

x^{2} + 8 y^{2} + 54 x - 48 y + 8 = 0

x^{2} + 2 y^{2} + 4 x + 18 y - 100 = 0

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