What is 4x^2+y^2+16x-6y-39=0 ?

The solution to 4x^2+y^2+16x-6y-39=0 is Ellipse with (h,k)=(-2,3),a=4,b=8

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4x^2+y^2+16x-6y-39=0

4 x^{2} + y^{2} + 16 x - 6 y - 39 = 0

(h, k) = (- 2, 3), a = 4, b = 8

Solution steps

4 x^{2} + y^{2} + 16 x - 6 y - 39 = 0

Rewrite

4 x^{2} + y^{2} + 16 x - 6 y - 39 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 3), a = 4, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 3), b = 8, a = 4

25 x^{2} + 81 y^{2} = 2025

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

\frac{( x - 2 ) ^{2}}{20} + \frac{y ^{2}}{36} = 1

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

\frac{( X - 1 ) ^{2}}{4} + \frac{( Y + 2 ) ^{2}}{16} = 1

What is 4x^2+y^2+16x-6y-39=0 ?
The solution to 4x^2+y^2+16x-6y-39=0 is Ellipse with (h,k)=(-2,3),a=4,b=8