What is 16x^2+81y^2=49 ?

The solution to 16x^2+81y^2=49 is Ellipse with (h,k)=(0,0),a= 7/4 ,b= 7/9

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16x^2+81y^2=49

16 x^{2} + 81 y^{2} = 49

(h, k) = (0, 0), a = \frac{7}{4}, b = \frac{7}{9}

Solution steps

16 x^{2} + 81 y^{2} = 49

Rewrite

16 x^{2} + 81 y^{2} = 49

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{9} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{4}, b = \frac{7}{9}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{7}{4}, b = \frac{7}{9}

\frac{x ^{2}}{1} + \frac{y ^{2}}{64} = 1

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

16 x^{2} + 25 y^{2} - 1600 = 0

\frac{2 x}{x ^{2} + y ^{2}} < - 1

\frac{1000}{1 + x ^{2} + y ^{2}} = 200

What is 16x^2+81y^2=49 ?
The solution to 16x^2+81y^2=49 is Ellipse with (h,k)=(0,0),a= 7/4 ,b= 7/9