What is 4x^2+9y^2-8x-54y-5=0 ?

The solution to 4x^2+9y^2-8x-54y-5=0 is Ellipse with (h,k)=(1,3),a=(3sqrt(5))/(sqrt(2)),b=sqrt(10)

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4x^2+9y^2-8x-54y-5=0

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0

(h, k) = (1, 3), a = \frac{3 5}{2}, b = 10

Solution steps

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0

Rewrite

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{3 5}{2} ) ^{2}} + \frac{( y - 3 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 3), a = \frac{3 5}{2}, b = 10

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = \frac{3 5}{2}, b = 10

x^{2} + 4 y^{2} + 8 x + 8 y - 16 = 0

9 x^{2} + 16 y^{2} - 160 y + 256 = 0

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

\frac{X ^{2}}{16} + (y - 4)^{2} = 1

What is 4x^2+9y^2-8x-54y-5=0 ?
The solution to 4x^2+9y^2-8x-54y-5=0 is Ellipse with (h,k)=(1,3),a=(3sqrt(5))/(sqrt(2)),b=sqrt(10)