What is 4x^2+9y^2-40x+54y+1+5=0 ?

The solution to 4x^2+9y^2-40x+54y+1+5=0 is Ellipse with (h,k)=(5,-3),a=(5sqrt(7))/2 ,b=(5sqrt(7))/3

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4x^2+9y^2-40x+54y+1+5=0

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

(h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

Solution steps

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

Rewrite

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( \frac{5 7}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{5 7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

25 x^{2} + 9 y^{2} - 100 x + 18 x - 116 = 0

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 6 ) ^{2}}{4} = 1

4 x^{2} + 9 y^{2} - 16 x - 18 y = 11

\frac{x ^{2}}{9} + \frac{z ^{2}}{49} = 1

What is 4x^2+9y^2-40x+54y+1+5=0 ?
The solution to 4x^2+9y^2-40x+54y+1+5=0 is Ellipse with (h,k)=(5,-3),a=(5sqrt(7))/2 ,b=(5sqrt(7))/3