What is 16x^2+25y^2= 169/4 ?

The solution to 16x^2+25y^2= 169/4 is Ellipse with (h,k)=(0,0),a= 13/8 ,b= 13/10

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16x^2+25y^2= 169/4

16 x^{2} + 25 y^{2} = \frac{169}{4}

(h, k) = (0, 0), a = \frac{13}{8}, b = \frac{13}{10}

Solution steps

16 x^{2} + 25 y^{2} = \frac{169}{4}

Rewrite

16 x^{2} + 25 y^{2} = \frac{169}{4}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{13}{8} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{13}{10} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{13}{8}, b = \frac{13}{10}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{13}{8}, b = \frac{13}{10}

\frac{( x - 3 ) ^{2}}{16} + (\frac{( y + 4 )}{9})^{2} = 1

9 x^{2} + 5 y^{2} = 180

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{29} = 1

\frac{( x - 4 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{10} = 1

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

What is 16x^2+25y^2= 169/4 ?
The solution to 16x^2+25y^2= 169/4 is Ellipse with (h,k)=(0,0),a= 13/8 ,b= 13/10