What is 49x^2+100y^2+882x-1400y+3969=0 ?

The solution to 49x^2+100y^2+882x-1400y+3969=0 is Ellipse with (h,k)=(-9,7),a=10,b=7

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49x^2+100y^2+882x-1400y+3969=0

49 x^{2} + 100 y^{2} + 882 x - 1400 y + 3969 = 0

(h, k) = (- 9, 7), a = 10, b = 7

Solution steps

49 x^{2} + 100 y^{2} + 882 x - 1400 y + 3969 = 0

Rewrite

49 x^{2} + 100 y^{2} + 882 x - 1400 y + 3969 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 9 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 7 ) ^{2}}{7 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 9, 7), a = 10, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 9, 7), a = 10, b = 7

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

x^{2} + 4 y^{2} = 64

\frac{25 x ^{2} + 16 y ^{2}}{400} = 1

\frac{y ^{2}}{16} + \frac{x ^{2}}{4} = 1

12 x^{2} + 8 y^{2} = 96

What is 49x^2+100y^2+882x-1400y+3969=0 ?
The solution to 49x^2+100y^2+882x-1400y+3969=0 is Ellipse with (h,k)=(-9,7),a=10,b=7