What is 16x^2+4y^2+96x-16y+96=0 ?

The solution to 16x^2+4y^2+96x-16y+96=0 is Ellipse with (h,k)=(-3,2),a=2,b=4

Popular >

16x^2+4y^2+96x-16y+96=0

16 x^{2} + 4 y^{2} + 96 x - 16 y + 96 = 0

(h, k) = (- 3, 2), a = 2, b = 4

Solution steps

16 x^{2} + 4 y^{2} + 96 x - 16 y + 96 = 0

Rewrite

16 x^{2} + 4 y^{2} + 96 x - 16 y + 96 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 2), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 2), b = 4, a = 2

\frac{( x + 1 ) ^{2}}{49} + \frac{( y - 7 ) ^{2}}{1} = 1

4 (x - 3)^{2} + 2 (y + 4)^{2} = 16

3 x^{2} - 12 x + y^{2} - 4 y + 1 = 0

(\frac{u + v}{u ^{2} + v ^{2}}) + (\frac{- v + u}{u ^{2} + v ^{2}}) = 1

3 x^{2} + 2 y^{2} - 6 = 0

What is 16x^2+4y^2+96x-16y+96=0 ?
The solution to 16x^2+4y^2+96x-16y+96=0 is Ellipse with (h,k)=(-3,2),a=2,b=4