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

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