What is 4x^2+y^2-48x+4y+48=0 ?

The solution to 4x^2+y^2-48x+4y+48=0 is Ellipse with (h,k)=(6,-2),a=5,b=10

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4x^2+y^2-48x+4y+48=0

4 x^{2} + y^{2} - 48 x + 4 y + 48 = 0

(h, k) = (6, - 2), a = 5, b = 10

Solution steps

4 x^{2} + y^{2} - 48 x + 4 y + 48 = 0

Rewrite

4 x^{2} + y^{2} - 48 x + 4 y + 48 = 0

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 2), a = 5, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (6, - 2), b = 10, a = 5

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

4 x^{2} + y^{2} - 36 x + 120 y + 80 = 0

- 2 p^{2} + 2 q + p = 3 q^{2} + q - 3 p - 2

2 X^{2} - 6 < - 6 Y^{2}

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

What is 4x^2+y^2-48x+4y+48=0 ?
The solution to 4x^2+y^2-48x+4y+48=0 is Ellipse with (h,k)=(6,-2),a=5,b=10