What is 4x^2+9y^2-40x+54y+145=0 ?

The solution to 4x^2+9y^2-40x+54y+145=0 is Ellipse with (h,k)=(5,-3),a=3,b=2

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4x^2+9y^2-40x+54y+145=0

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

(h, k) = (5, - 3), a = 3, b = 2

Solution steps

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

Rewrite

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 3), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = 3, b = 2

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

\frac{( x - 100 ) ^{2}}{400} + \frac{( y - 90 ) ^{2}}{900} = 1

16 x^{2} + y^{2} = 64

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

What is 4x^2+9y^2-40x+54y+145=0 ?
The solution to 4x^2+9y^2-40x+54y+145=0 is Ellipse with (h,k)=(5,-3),a=3,b=2