What is 4x^2+y^2+8x+4y-4=0 ?

The solution to 4x^2+y^2+8x+4y-4=0 is Ellipse with (h,k)=(-1,-2),a=sqrt(3),b=2sqrt(3)

Popular >

4x^2+y^2+8x+4y-4=0

4 x^{2} + y^{2} + 8 x + 4 y - 4 = 0

(h, k) = (- 1, - 2), a = 3, b = 23

Solution steps

4 x^{2} + y^{2} + 8 x + 4 y - 4 = 0

Rewrite

4 x^{2} + y^{2} + 8 x + 4 y - 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 2), a = 3, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 2), b = 23, a = 3

\frac{x ^{2}}{1} + \frac{y ^{2}}{a - 16} = 1

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

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

\frac{( y + 3 ) ^{2}}{25} + \frac{( x + 4 ) ^{2}}{16} = 1

What is 4x^2+y^2+8x+4y-4=0 ?
The solution to 4x^2+y^2+8x+4y-4=0 is Ellipse with (h,k)=(-1,-2),a=sqrt(3),b=2sqrt(3)