What is 16x^2+25y^2=1.6 ?

The solution to 16x^2+25y^2=1.6 is Ellipse with (h,k)=(0,0),a=0.31622…,b=0.25298…

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16x^2+25y^2=1.6

16 x^{2} + 25 y^{2} = 1.6

(h, k) = (0, 0), a = 0.31622 \dots, b = 0.25298 \dots

Solution steps

16 x^{2} + 25 y^{2} = 1.6

Rewrite

16 x^{2} + 25 y^{2} = 1.6

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{0.31622 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{0.25298 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 0.31622 \dots, b = 0.25298 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 0.31622 \dots, b = 0.25298 \dots

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

16 x^{2} + 9 y^{2} + 160 x + 18 y + 265 = 0

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

x^{2} + \frac{y ^{2}}{25} = 1

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1

What is 16x^2+25y^2=1.6 ?
The solution to 16x^2+25y^2=1.6 is Ellipse with (h,k)=(0,0),a=0.31622…,b=0.25298…