What is 3x^2+4y^2-18x-8y-17=0 ?

The solution to 3x^2+4y^2-18x-8y-17=0 is Ellipse with (h,k)=(3,1),a=4,b=2sqrt(3)

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3x^2+4y^2-18x-8y-17=0

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

(h, k) = (3, 1), a = 4, b = 23

Solution steps

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

Rewrite

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 1), a = 4, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 1), a = 4, b = 23

\frac{x ^{2}}{20} + \frac{y ^{2}}{16} = 1

\frac{( x + 7 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1

49 x^{2} + y^{2} - 14 y = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 4

x^{2} + 5 y^{2} = 2021 y

What is 3x^2+4y^2-18x-8y-17=0 ?
The solution to 3x^2+4y^2-18x-8y-17=0 is Ellipse with (h,k)=(3,1),a=4,b=2sqrt(3)