What is 4x^2+y^2+16x+16y-64=0 ?

The solution to 4x^2+y^2+16x+16y-64=0 is Ellipse with (h,k)=(-2,-8),a=6,b=12

Popular >

4x^2+y^2+16x+16y-64=0

4 x^{2} + y^{2} + 16 x + 16 y - 64 = 0

(h, k) = (- 2, - 8), a = 6, b = 12

Solution steps

4 x^{2} + y^{2} + 16 x + 16 y - 64 = 0

Rewrite

4 x^{2} + y^{2} + 16 x + 16 y - 64 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{6 ^{2}} + \frac{( y - ( - 8 ) ) ^{2}}{1 2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 8), a = 6, b = 12

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 8), b = 12, a = 6

5 x^{2} + 9 y^{2} - 10 x - 36 y = 4

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

\frac{( x + 2 ) ^{2}}{15} + \frac{y ^{2}}{64} = 1

(x^{2} + 8 x) + (3 y^{2} + 8 y) = 11

\frac{( x + 2 ) ^{2}}{20} + \frac{( y - 3 ) ^{2}}{4} = 1

What is 4x^2+y^2+16x+16y-64=0 ?
The solution to 4x^2+y^2+16x+16y-64=0 is Ellipse with (h,k)=(-2,-8),a=6,b=12