What is 9x^2+16y^2<25 ?

The solution to 9x^2+16y^2<25 is Ellipse with (h,k)=(0,0),a= 5/3 ,b= 5/4

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9x^2+16y^2<25

9 x^{2} + 16 y^{2} < 25

(h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

Solution steps

9 x^{2} + 16 y^{2} < 25

Rewrite

9 x^{2} + 16 y^{2} < 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

4 x^{2} + y^{2} - 8 x + 4 y + 4 = 0

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0

What is 9x^2+16y^2<25 ?
The solution to 9x^2+16y^2<25 is Ellipse with (h,k)=(0,0),a= 5/3 ,b= 5/4