What is 49x^2+4y^2+98x-147=0 ?

The solution to 49x^2+4y^2+98x-147=0 is Ellipse with (h,k)=(-1,0),a=2,b=7

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49x^2+4y^2+98x-147=0

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

(h, k) = (- 1, 0), a = 2, b = 7

Solution steps

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

Rewrite

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 2, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 7, a = 2

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

2 x - x^{2} - 4 y^{2} - 16 y - 1 = 0

\frac{( x - 4 ) ^{2}}{16} + \frac{y ^{2}}{40.96} = 1

2 x^{2} + 2 y^{2} - 28 y = 0

What is 49x^2+4y^2+98x-147=0 ?
The solution to 49x^2+4y^2+98x-147=0 is Ellipse with (h,k)=(-1,0),a=2,b=7