What is 9x^2+25y^2-36x-50y-164=0 ?

The solution to 9x^2+25y^2-36x-50y-164=0 is Ellipse with (h,k)=(2,1),a=5,b=3

Popular >

9x^2+25y^2-36x-50y-164=0

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

(h, k) = (2, 1), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 5, b = 3

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

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

\frac{( y - 2 ) ^{2}}{9} + \frac{( x - 3 ) ^{2}}{16} = 1

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{4} = 1

6 x^{2} + 96 x + 16 y^{2} - 40 y = 315

What is 9x^2+25y^2-36x-50y-164=0 ?
The solution to 9x^2+25y^2-36x-50y-164=0 is Ellipse with (h,k)=(2,1),a=5,b=3