What is 7x^{(2)}+10y^{(2)}-56x+100y+292=0 ?

The solution to 7x^{(2)}+10y^{(2)}-56x+100y+292=0 is Ellipse with (h,k)=(4,-5),a=sqrt(10),b=sqrt(7)

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7x^{(2)}+10y^{(2)}-56x+100y+292=0

7 x^{(2)} + 10 y^{(2)} - 56 x + 100 y + 292 = 0

(h, k) = (4, - 5), a = 10, b = 7

Solution steps

7 x^{2} + 10 y^{2} - 56 x + 100 y + 292 = 0

Rewrite

7 x^{2} + 10 y^{2} - 56 x + 100 y + 292 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 5), a = 10, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 5), a = 10, b = 7

\frac{x ^{2}}{17} + \frac{y ^{2}}{15} = 1

5 x^{2} + 7 y^{2} = 70

\frac{3 x ^{2}}{4} + (\frac{4 y}{4})^{2} = \frac{12}{12}

9 x^{2} + 25 y^{2} - 18 x - 250 y + 409 = 0

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

What is 7x^{(2)}+10y^{(2)}-56x+100y+292=0 ?
The solution to 7x^{(2)}+10y^{(2)}-56x+100y+292=0 is Ellipse with (h,k)=(4,-5),a=sqrt(10),b=sqrt(7)