What is x^2+4y^2-6x-55=0 ?

The solution to x^2+4y^2-6x-55=0 is Ellipse with (h,k)=(3,0),a=8,b=4

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x^2+4y^2-6x-55=0

x^{2} + 4 y^{2} - 6 x - 55 = 0

(h, k) = (3, 0), a = 8, b = 4

Solution steps

x^{2} + 4 y^{2} - 6 x - 55 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x - 55 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{8 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 0), a = 8, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 0), a = 8, b = 4

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

(\frac{x - 2}{4})^{2} + (\frac{y + 3}{16})^{2} = 1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{\frac{25}{4}} = 1

(x - 2)^{2} + 4 y^{2} = 4

What is x^2+4y^2-6x-55=0 ?
The solution to x^2+4y^2-6x-55=0 is Ellipse with (h,k)=(3,0),a=8,b=4