What is 49x^2+9y^2=16 ?

The solution to 49x^2+9y^2=16 is Ellipse with (h,k)=(0,0),a= 4/7 ,b= 4/3

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49x^2+9y^2=16

49 x^{2} + 9 y^{2} = 16

(h, k) = (0, 0), a = \frac{4}{7}, b = \frac{4}{3}

Solution steps

49 x^{2} + 9 y^{2} = 16

Rewrite

49 x^{2} + 9 y^{2} = 16

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4}{7} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{4}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{4}{7}, b = \frac{4}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{4}{3}, a = \frac{4}{7}

\frac{( x - 3 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{32} = 1

x^{2} + 4 y^{2} - 20 x + 84 = 0

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 (x^{2} + y^{2} - 4 x - 8 y + 20)

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

3 x^{2} + y^{2} + 12 x - 2 y + 1 = 0

What is 49x^2+9y^2=16 ?
The solution to 49x^2+9y^2=16 is Ellipse with (h,k)=(0,0),a= 4/7 ,b= 4/3