What is x^2+4x+2y^2+6y+1=0 ?

The solution to x^2+4x+2y^2+6y+1=0 is Ellipse with (h,k)=(-2,-3/2),a=sqrt(15/2),b=(sqrt(15))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2+4x+2y^2+6y+1=0

x^{2} + 4 x + 2 y^{2} + 6 y + 1 = 0

(h, k) = (- 2, - \frac{3}{2}), a = \frac{15}{2}, b = \frac{15}{2}

Solution steps

x^{2} + 4 x + 2 y^{2} + 6 y + 1 = 0

Rewrite

x^{2} + 4 x + 2 y^{2} + 6 y + 1 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{15}{2} ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{15}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - \frac{3}{2}), a = \frac{15}{2}, b = \frac{15}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - \frac{3}{2}), a = \frac{15}{2}, b = \frac{15}{2}

2 \cdot x^{2} + y^{2} = 6

20 x^{2} + 36 y^{2} = 405

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{4}

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

\frac{( ( x - 2 ) ^{2} )}{4} + \frac{( ( y + 4 ) ^{2} )}{16} = 1

What is x^2+4x+2y^2+6y+1=0 ?
The solution to x^2+4x+2y^2+6y+1=0 is Ellipse with (h,k)=(-2,-3/2),a=sqrt(15/2),b=(sqrt(15))/2