What is 28x^2+64y^2-84x-49=0 ?

The solution to 28x^2+64y^2-84x-49=0 is Ellipse with (h,k)=(3/2 ,0),a=2,b=(sqrt(7))/2

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28x^2+64y^2-84x-49=0

28 x^{2} + 64 y^{2} - 84 x - 49 = 0

(h, k) = (\frac{3}{2}, 0), a = 2, b = \frac{7}{2}

Solution steps

28 x^{2} + 64 y^{2} - 84 x - 49 = 0

Rewrite

28 x^{2} + 64 y^{2} - 84 x - 49 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, 0), a = 2, b = \frac{7}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, 0), a = 2, b = \frac{7}{2}

9 x^{2} + 4 y^{2} - 36 x - 24 y + 36 = 0

9 x^{2} + 25 y^{2} - 54 x - 100 y - 44 = 0

\frac{( x ^{2} - 4 x )}{4} + \frac{( y ^{2} - 6 y )}{9} = - 1

2 x^{2} + 4 y^{2} + 10 x + 8 y - 9 = 0

2 x^{2} + 5 y^{2} = 9

What is 28x^2+64y^2-84x-49=0 ?
The solution to 28x^2+64y^2-84x-49=0 is Ellipse with (h,k)=(3/2 ,0),a=2,b=(sqrt(7))/2