What is 13x^2-10x+2+y^2=4x-1 ?

The solution to 13x^2-10x+2+y^2=4x-1 is Ellipse with (h,k)=(7/13 ,0),a=(sqrt(10))/(13),b=sqrt(10/13)

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13x^2-10x+2+y^2=4x-1

13 x^{2} - 10 x + 2 + y^{2} = 4 x - 1

(h, k) = (\frac{7}{13}, 0), a = \frac{10}{13}, b = \frac{10}{13}

Solution steps

13 x^{2} - 10 x + 2 + y^{2} = 4 x - 1

Rewrite

13 x^{2} - 10 x + 2 + y^{2} - 4 x + 1 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{7}{13} ) ^{2}}{( \frac{10}{13} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{10}{13} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{7}{13}, 0), a = \frac{10}{13}, b = \frac{10}{13}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{7}{13}, 0), b = \frac{10}{13}, a = \frac{10}{13}

8 x^{2} + 9 y^{2} = 72

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60 x^{2} + 108 y^{2} = 6480

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

2 x^{2} + 2 y^{2} + 36 y = 0

What is 13x^2-10x+2+y^2=4x-1 ?
The solution to 13x^2-10x+2+y^2=4x-1 is Ellipse with (h,k)=(7/13 ,0),a=(sqrt(10))/(13),b=sqrt(10/13)