What is 16x^2+15y^2-64x-90y-41=0 ?

The solution to 16x^2+15y^2-64x-90y-41=0 is Ellipse with (h,k)=(2,3),a=sqrt(15),b=4

Popular >

16x^2+15y^2-64x-90y-41=0

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

(h, k) = (2, 3), a = 15, b = 4

Solution steps

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

Rewrite

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 15 ) ^{2}} + \frac{( y - 3 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 3), a = 15, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 3), b = 4, a = 15

25 y^{2} + 9 x^{2} - 108 x - 200 y + 499 = 0

50 = \frac{100}{1 + x ^{2} + y ^{2}}

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9989 8 ^{2}} = 1

9 x^{2} + 25 y^{2} + 90 x = 0

What is 16x^2+15y^2-64x-90y-41=0 ?
The solution to 16x^2+15y^2-64x-90y-41=0 is Ellipse with (h,k)=(2,3),a=sqrt(15),b=4