What is 36x^2+16y^2+180x-24y+90=0 ?

The solution to 36x^2+16y^2+180x-24y+90=0 is Ellipse with (h,k)=(-5/2 , 3/4),a=2,b=3

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36x^2+16y^2+180x-24y+90=0

36 x^{2} + 16 y^{2} + 180 x - 24 y + 90 = 0

(h, k) = (- \frac{5}{2}, \frac{3}{4}), a = 2, b = 3

Solution steps

36 x^{2} + 16 y^{2} + 180 x - 24 y + 90 = 0

Rewrite

36 x^{2} + 16 y^{2} + 180 x - 24 y + 90 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{5}{2}, \frac{3}{4}), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{5}{2}, \frac{3}{4}), b = 3, a = 2

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

x^{2} + 3 y^{2} - 3 x - 5 y = 0

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

What is 36x^2+16y^2+180x-24y+90=0 ?
The solution to 36x^2+16y^2+180x-24y+90=0 is Ellipse with (h,k)=(-5/2 , 3/4),a=2,b=3