What is 16x^2+9y^2+160x+18y+265=0 ?

The solution to 16x^2+9y^2+160x+18y+265=0 is Ellipse with (h,k)=(-5,-1),a=3,b=4

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16x^2+9y^2+160x+18y+265=0

16 x^{2} + 9 y^{2} + 160 x + 18 y + 265 = 0

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

Solution steps

16 x^{2} + 9 y^{2} + 160 x + 18 y + 265 = 0

Rewrite

16 x^{2} + 9 y^{2} + 160 x + 18 y + 265 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(\frac{x ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

x^{2} + \frac{y ^{2}}{25} = 1

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1

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

- \frac{x ^{2}}{4} - \frac{z ^{2}}{4} = 1

What is 16x^2+9y^2+160x+18y+265=0 ?
The solution to 16x^2+9y^2+160x+18y+265=0 is Ellipse with (h,k)=(-5,-1),a=3,b=4