What is 16x^2+y^2+64x+4y+52=0 ?

The solution to 16x^2+y^2+64x+4y+52=0 is Ellipse with (h,k)=(-2,-2),a=1,b=4

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16x^2+y^2+64x+4y+52=0

16 x^{2} + y^{2} + 64 x + 4 y + 52 = 0

(h, k) = (- 2, - 2), a = 1, b = 4

Solution steps

16 x^{2} + y^{2} + 64 x + 4 y + 52 = 0

Rewrite

16 x^{2} + y^{2} + 64 x + 4 y + 52 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 2), a = 1, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 2), b = 4, a = 1

7 x^{2} + 4 y^{2} + 24 y = - 8

\frac{x ^{2}}{95} + \frac{y ^{2}}{30} = 1

20 x^{2} + 25 y^{2} = 400

x^{2} + 4 y^{2} - 8 x + 16 y + 16 = 0

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

What is 16x^2+y^2+64x+4y+52=0 ?
The solution to 16x^2+y^2+64x+4y+52=0 is Ellipse with (h,k)=(-2,-2),a=1,b=4