What is (2x-y)(3x-y)=6x2-5xy+y2 ?

The solution to (2x-y)(3x-y)=6x2-5xy+y2 is Ellipse with (h,k)=(1,1),a=sqrt(7/6),b=sqrt(7)

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(2x-y)(3x-y)=6x2-5xy+y2

(2 x - y) (3 x - y) = 6 x 2 - 5 x y + y 2

(h, k) = (1, 1), a = \frac{7}{6}, b = 7

Solution steps

(2 x - y) (3 x - y) = 6 x \cdot 2 - 5 x y + y \cdot 2

Rewrite

(2 x - y) (3 x - y) - 6 x 2 + 5 x y - y 2 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{7}{6} ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 1), a = \frac{7}{6}, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 1), b = 7, a = \frac{7}{6}

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

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

9 x^{2} + 81 y^{2} - 729 = 0

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

What is (2x-y)(3x-y)=6x2-5xy+y2 ?
The solution to (2x-y)(3x-y)=6x2-5xy+y2 is Ellipse with (h,k)=(1,1),a=sqrt(7/6),b=sqrt(7)