What is 49x^2+16y^2=784 ?

The solution to 49x^2+16y^2=784 is Ellipse with (h,k)=(0,0),a=4,b=7

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49x^2+16y^2=784

49 x^{2} + 16 y^{2} = 784

(h, k) = (0, 0), a = 4, b = 7

Solution steps

49 x^{2} + 16 y^{2} = 784

Rewrite

49 x^{2} + 16 y^{2} = 784

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{7 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, 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 = 4

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

9 x^{2} + 4 y^{2} - 18 x + 8 y + 4 = 0

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

3 x^{2} + 5 y^{2} - 12 x + 30 y = - 42

What is 49x^2+16y^2=784 ?
The solution to 49x^2+16y^2=784 is Ellipse with (h,k)=(0,0),a=4,b=7