What is (17x^2+9y^2-30y+9)/(16)=0 ?

The solution to (17x^2+9y^2-30y+9)/(16)=0 is Ellipse with (h,k)=(0, 5/3),a= 4/(sqrt(17)),b= 4/3

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(17x^2+9y^2-30y+9)/(16)=0

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

(h, k) = (0, \frac{5}{3}), a = \frac{4}{17}, b = \frac{4}{3}

Solution steps

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

Rewrite

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4}{17} ) ^{2}} + \frac{( y - \frac{5}{3} ) ^{2}}{( \frac{4}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{5}{3}), a = \frac{4}{17}, b = \frac{4}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{5}{3}), b = \frac{4}{3}, a = \frac{4}{17}

9 = \frac{1}{x ^{2} + y ^{2} - 7}

x^{2} + 8 y^{2} - 12 x - 16 y - 36 = 0

\frac{( x - 3 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{5} = 1

\frac{( x ^{(2)} )}{( 36 )} + \frac{( y ^{(2)} )}{( 16 )} = 1

16 x^{2} + 36 y^{2} - 256 x + 576 y + 2752 = 0

What is (17x^2+9y^2-30y+9)/(16)=0 ?
The solution to (17x^2+9y^2-30y+9)/(16)=0 is Ellipse with (h,k)=(0, 5/3),a= 4/(sqrt(17)),b= 4/3