What is 9x^2+25y^2-18x-100y-3=0 ?

The solution to 9x^2+25y^2-18x-100y-3=0 is Ellipse with (h,k)=(1,2),a=(4sqrt(7))/3 ,b=(4sqrt(7))/5

Popular >

9x^2+25y^2-18x-100y-3=0

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

(h, k) = (1, 2), a = \frac{4 7}{3}, b = \frac{4 7}{5}

Solution steps

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

Rewrite

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{4 7}{3} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{4 7}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 2), a = \frac{4 7}{3}, b = \frac{4 7}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = \frac{4 7}{3}, b = \frac{4 7}{5}

(\frac{x ^{2}}{a ^{2}}) + (\frac{y ^{2}}{b ^{2}}) = 1

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{y ^{2}}{9} = 1 - \frac{x ^{2}}{4}

8 = \frac{1}{2} x^{2} + \frac{1}{4} y^{2}

What is 9x^2+25y^2-18x-100y-3=0 ?
The solution to 9x^2+25y^2-18x-100y-3=0 is Ellipse with (h,k)=(1,2),a=(4sqrt(7))/3 ,b=(4sqrt(7))/5