What is (4x^2)+(y^2)-8x-4y-28=0 ?

The solution to (4x^2)+(y^2)-8x-4y-28=0 is Ellipse with (h,k)=(1,2),a=3,b=6

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(4x^2)+(y^2)-8x-4y-28=0

(4 x^{2}) + (y^{2}) - 8 x - 4 y - 28 = 0

(h, k) = (1, 2), a = 3, b = 6

Solution steps

4 x^{2} + y^{2} - 8 x - 4 y - 28 = 0

Rewrite

4 x^{2} + y^{2} - 8 x - 4 y - 28 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 6, a = 3

112 x^{2} + 144 y^{2} - 896 x + 864 y = - 2080

8 x^{2} + y^{2} = 1

9 = 4 x^{2} + z^{2}

\frac{x ^{2}}{4} + \frac{y ^{2}}{6} = 1

9 x^{2} + 16 y^{2} - 54 x - 64 y + 1 = 0

What is (4x^2)+(y^2)-8x-4y-28=0 ?
The solution to (4x^2)+(y^2)-8x-4y-28=0 is Ellipse with (h,k)=(1,2),a=3,b=6