What is 49x^2+4y^2=196 ?

The solution to 49x^2+4y^2=196 is Ellipse with (h,k)=(0,0),a=2,b=7

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49x^2+4y^2=196

49 x^{2} + 4 y^{2} = 196

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

Solution steps

49 x^{2} + 4 y^{2} = 196

Rewrite

49 x^{2} + 4 y^{2} = 196

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1

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

2 x^{2} + y^{2} \leq 1

\frac{x ^{2}}{7 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

16 x^{2} + 25 y^{2} - 64 x + 150 y = - 279

What is 49x^2+4y^2=196 ?
The solution to 49x^2+4y^2=196 is Ellipse with (h,k)=(0,0),a=2,b=7