What is 16x^2+y^2+96x-10y=-153 ?

The solution to 16x^2+y^2+96x-10y=-153 is Ellipse with (h,k)=(-3,5),a=1,b=4

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16x^2+y^2+96x-10y=-153

16 x^{2} + y^{2} + 96 x - 10 y = - 153

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

Solution steps

16 x^{2} + y^{2} + 96 x - 10 y = - 153

Rewrite

16 x^{2} + y^{2} + 96 x - 10 y = - 153

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + y^{2} - 25 = \frac{x + 25}{7} - y

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

(y - 6)^{2} = 23 - \frac{23 ( x - 3 ) ^{2}}{39}

\frac{x ^{2}}{1.58 7 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

9 \cdot (x - 1)^{2} + 4 \cdot y^{2} = 36

What is 16x^2+y^2+96x-10y=-153 ?
The solution to 16x^2+y^2+96x-10y=-153 is Ellipse with (h,k)=(-3,5),a=1,b=4