What is 16x^2-96x+5y^2+10y+69=0 ?

The solution to 16x^2-96x+5y^2+10y+69=0 is Ellipse with (h,k)=(3,-1),a=sqrt(5),b=4

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16x^2-96x+5y^2+10y+69=0

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

(h, k) = (3, - 1), a = 5, b = 4

Solution steps

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

Rewrite

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 5, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), b = 4, a = 5

\frac{x ^{2}}{1} + \frac{y ^{2}}{1 - 16} = 1

x^{2} + y^{2} \geq - 4 y

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{3} = 1

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

2 x^{2} + 2 y^{2} - 24 y = 0

What is 16x^2-96x+5y^2+10y+69=0 ?
The solution to 16x^2-96x+5y^2+10y+69=0 is Ellipse with (h,k)=(3,-1),a=sqrt(5),b=4