What is 100x^2+64y^2<1600 ?

The solution to 100x^2+64y^2<1600 is Ellipse with (h,k)=(0,0),a=4,b=5

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100x^2+64y^2<1600

100 x^{2} + 64 y^{2} < 1600

(h, k) = (0, 0), a = 4, b = 5

Solution steps

100 x^{2} + 64 y^{2} < 1600

Rewrite

100 x^{2} + 64 y^{2} < 1600

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 4

9 x^{2} + 4 y^{2} + 90 x + 8 y + 193 = 0

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

2 x^{2} + y^{2} - 2 x + 16 y + 1 = 0

x^{2} + y^{2} + 2 y \leq 0

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

What is 100x^2+64y^2<1600 ?
The solution to 100x^2+64y^2<1600 is Ellipse with (h,k)=(0,0),a=4,b=5