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

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

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

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

(h, k) = (3, - 2), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), b = 4, a = 2

\frac{x - 3 y}{x ^{2} + y ^{2}} + 1 = 0

a^{2} + \frac{a ^{2}}{2} + \frac{b ^{2}}{2} = 26

x^{2} + y^{2} = - 12 y

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

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

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