What is 16x^2+25y^2+32x-384=0 ?

The solution to 16x^2+25y^2+32x-384=0 is Ellipse with (h,k)=(-1,0),a=5,b=4

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16x^2+25y^2+32x-384=0

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

(h, k) = (- 1, 0), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

Rewrite

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), a = 5, b = 4

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

x^{2} + 2 y^{2} = 1

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

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

2 x^{2} + y^{2} = 50

What is 16x^2+25y^2+32x-384=0 ?
The solution to 16x^2+25y^2+32x-384=0 is Ellipse with (h,k)=(-1,0),a=5,b=4