What is 4x^2+y^2-24x-8y+8=0 ?

The solution to 4x^2+y^2-24x-8y+8=0 is Ellipse with (h,k)=(3,4),a=sqrt(11),b=2sqrt(11)

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4x^2+y^2-24x-8y+8=0

4 x^{2} + y^{2} - 24 x - 8 y + 8 = 0

(h, k) = (3, 4), a = 11, b = 211

Solution steps

4 x^{2} + y^{2} - 24 x - 8 y + 8 = 0

Rewrite

4 x^{2} + y^{2} - 24 x - 8 y + 8 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 11 ) ^{2}} + \frac{( y - 4 ) ^{2}}{( 2 11 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 4), a = 11, b = 211

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 4), b = 211, a = 11

1 = x^{2} + 3 y^{2}

4 x^{2} + y^{2} - 24 x + 2 y + 21 = 0

x^{2} + 5 y^{2} = \frac{1}{5}

9 x^{2} + 4 y^{2} + 18 x - 40 y + 73 = 0

\frac{( x + 8 ) ^{2}}{64} + \frac{( y - 11 ) ^{2}}{36} = 1

What is 4x^2+y^2-24x-8y+8=0 ?
The solution to 4x^2+y^2-24x-8y+8=0 is Ellipse with (h,k)=(3,4),a=sqrt(11),b=2sqrt(11)