What is 4x^{(2)}+16y^{(2)}-16x-48=0 ?

The solution to 4x^{(2)}+16y^{(2)}-16x-48=0 is Ellipse with (h,k)=(2,0),a=4,b=2

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4x^{(2)}+16y^{(2)}-16x-48=0

4 x^{(2)} + 16 y^{(2)} - 16 x - 48 = 0

(h, k) = (2, 0), a = 4, b = 2

Solution steps

4 x^{2} + 16 y^{2} - 16 x - 48 = 0

Rewrite

4 x^{2} + 16 y^{2} - 16 x - 48 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 4, b = 2

\frac{( x ^{2} )}{( 16 )} + \frac{( y ^{2} )}{( 12 )} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 7 ) ^{2}}{64} = 1

2 x^{2} + 3 y^{2} + 4 x = 19

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

25 y^{2} + 36 (x - 8)^{2} = 900

What is 4x^{(2)}+16y^{(2)}-16x-48=0 ?
The solution to 4x^{(2)}+16y^{(2)}-16x-48=0 is Ellipse with (h,k)=(2,0),a=4,b=2