What is 36x^2+9y^2+48x-36y+43=0 ?

The solution to 36x^2+9y^2+48x-36y+43=0 is Ellipse with (h,k)=(-2/3 ,2),a= 1/2 ,b=1

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36x^2+9y^2+48x-36y+43=0

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

(h, k) = (- \frac{2}{3}, 2), a = \frac{1}{2}, b = 1

Solution steps

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

Rewrite

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{2}{3}, 2), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{2}{3}, 2), b = 1, a = \frac{1}{2}

What is 36x^2+9y^2+48x-36y+43=0 ?
The solution to 36x^2+9y^2+48x-36y+43=0 is Ellipse with (h,k)=(-2/3 ,2),a= 1/2 ,b=1