What is 4x^2+y^2-40x+4y+68=0 ?

The solution to 4x^2+y^2-40x+4y+68=0 is Ellipse with (h,k)=(5,-2),a=3,b=6

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4x^2+y^2-40x+4y+68=0

4 x^{2} + y^{2} - 40 x + 4 y + 68 = 0

(h, k) = (5, - 2), a = 3, b = 6

Solution steps

4 x^{2} + y^{2} - 40 x + 4 y + 68 = 0

Rewrite

4 x^{2} + y^{2} - 40 x + 4 y + 68 = 0

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), b = 6, a = 3

x^{2} + 2 x = - 4 y^{2} + 12 y + 7

x^{2} + 3 y^{2} + 10 x + 9 y - 20 = 0

\frac{( x + 1 ) ^{2}}{32} + \frac{( y + 5 ) ^{2}}{36} = 1

\frac{( x - 6 ) ^{2}}{122} + \frac{( y - 8 ) ^{2}}{\frac{12200}{121}} = 1

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

What is 4x^2+y^2-40x+4y+68=0 ?
The solution to 4x^2+y^2-40x+4y+68=0 is Ellipse with (h,k)=(5,-2),a=3,b=6