What is 4x^2+y^2+12x+6y+5=0 ?

The solution to 4x^2+y^2+12x+6y+5=0 is Ellipse with (h,k)=(-3/2 ,-3),a=(sqrt(13))/2 ,b=sqrt(13)

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4x^2+y^2+12x+6y+5=0

4 x^{2} + y^{2} + 12 x + 6 y + 5 = 0

(h, k) = (- \frac{3}{2}, - 3), a = \frac{13}{2}, b = 13

Solution steps

4 x^{2} + y^{2} + 12 x + 6 y + 5 = 0

Rewrite

4 x^{2} + y^{2} + 12 x + 6 y + 5 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{( \frac{13}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 13 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{3}{2}, - 3), a = \frac{13}{2}, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{3}{2}, - 3), b = 13, a = \frac{13}{2}

2 y^{2} + 4 z^{2} = 4

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

\frac{x ^{2}}{2 2 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

(x + 5)^{2} + \frac{3}{10} y^{2} = 34

4 - 2 x^{2} - 3 y^{2} = 0

What is 4x^2+y^2+12x+6y+5=0 ?
The solution to 4x^2+y^2+12x+6y+5=0 is Ellipse with (h,k)=(-3/2 ,-3),a=(sqrt(13))/2 ,b=sqrt(13)