What is 4x^2-8x+16y^2-96y+84=0 ?

The solution to 4x^2-8x+16y^2-96y+84=0 is Ellipse with (h,k)=(1,3),a=4,b=2

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4x^2-8x+16y^2-96y+84=0

4 x^{2} - 8 x + 16 y^{2} - 96 y + 84 = 0

(h, k) = (1, 3), a = 4, b = 2

Solution steps

4 x^{2} - 8 x + 16 y^{2} - 96 y + 84 = 0

Rewrite

4 x^{2} - 8 x + 16 y^{2} - 96 y + 84 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 3), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = 4, b = 2

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

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

\frac{( x ^{2} )}{9} + \frac{( y ^{2} )}{4} = 1

x^{2} 8 + \frac{y ^{2}}{7 ^{2}} = 1

\frac{x ^{2}}{24} + \frac{y ^{2}}{49} = 1

What is 4x^2-8x+16y^2-96y+84=0 ?
The solution to 4x^2-8x+16y^2-96y+84=0 is Ellipse with (h,k)=(1,3),a=4,b=2