What is 3x^2+7y^2-12x-28y+19=0 ?

The solution to 3x^2+7y^2-12x-28y+19=0 is Ellipse with (h,k)=(2,2),a=sqrt(7),b=sqrt(3)

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3x^2+7y^2-12x-28y+19=0

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

(h, k) = (2, 2), a = 7, b = 3

Solution steps

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

Rewrite

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 2), a = 7, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 2), a = 7, b = 3

16 x^{2} + 25 y^{2} = 1600

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

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

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

What is 3x^2+7y^2-12x-28y+19=0 ?
The solution to 3x^2+7y^2-12x-28y+19=0 is Ellipse with (h,k)=(2,2),a=sqrt(7),b=sqrt(3)