What is 4x^2-24x+(y^2)/(16)+y/8+573/16 =0 ?

The solution to 4x^2-24x+(y^2)/(16)+y/8+573/16 =0 is Ellipse with (h,k)=(3,-1),a= 1/4 ,b=2

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4x^2-24x+(y^2)/(16)+y/8+573/16 =0

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

(h, k) = (3, - 1), a = \frac{1}{4}, b = 2

Solution steps

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

Rewrite

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = \frac{1}{4}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), b = 2, a = \frac{1}{4}

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 7 ) ^{2}}{49} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

9 x^{2} + 5 y^{2} = 45

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

What is 4x^2-24x+(y^2)/(16)+y/8+573/16 =0 ?
The solution to 4x^2-24x+(y^2)/(16)+y/8+573/16 =0 is Ellipse with (h,k)=(3,-1),a= 1/4 ,b=2