What is 36x^2+16y^2+144x-160y-32=0 ?

The solution to 36x^2+16y^2+144x-160y-32=0 is Ellipse with (h,k)=(-2,5),a=4,b=6

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36x^2+16y^2+144x-160y-32=0

36 x^{2} + 16 y^{2} + 144 x - 160 y - 32 = 0

(h, k) = (- 2, 5), a = 4, b = 6

Solution steps

36 x^{2} + 16 y^{2} + 144 x - 160 y - 32 = 0

Rewrite

36 x^{2} + 16 y^{2} + 144 x - 160 y - 32 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 5), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 5), b = 6, a = 4

What is 36x^2+16y^2+144x-160y-32=0 ?
The solution to 36x^2+16y^2+144x-160y-32=0 is Ellipse with (h,k)=(-2,5),a=4,b=6