What is 16x^2+49y^2=25 ?

The solution to 16x^2+49y^2=25 is Ellipse with (h,k)=(0,0),a= 5/4 ,b= 5/7

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16x^2+49y^2=25

16 x^{2} + 49 y^{2} = 25

(h, k) = (0, 0), a = \frac{5}{4}, b = \frac{5}{7}

Solution steps

16 x^{2} + 49 y^{2} = 25

Rewrite

16 x^{2} + 49 y^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{4}, b = \frac{5}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{4}, b = \frac{5}{7}

What is 16x^2+49y^2=25 ?
The solution to 16x^2+49y^2=25 is Ellipse with (h,k)=(0,0),a= 5/4 ,b= 5/7