What is 5x^2+3y^2-40x-36y+158=0 ?

The solution to 5x^2+3y^2-40x-36y+158=0 is Ellipse with (h,k)=(4,6),a=sqrt(6),b=sqrt(10)

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5x^2+3y^2-40x-36y+158=0

5 x^{2} + 3 y^{2} - 40 x - 36 y + 158 = 0

(h, k) = (4, 6), a = 6, b = 10

Solution steps

5 x^{2} + 3 y^{2} - 40 x - 36 y + 158 = 0

Rewrite

5 x^{2} + 3 y^{2} - 40 x - 36 y + 158 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 6 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 6), a = 6, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 6), b = 10, a = 6

x^{2} + 64 y^{2} = 64

3 x^{2} + 4 y^{2} + 12 x - 8 y + 9 = 0

3 x^{2} + 5 y^{2} - 6 x + 8 y - 7 = 0

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

5 x^{2} + 9 y^{2} = 81

What is 5x^2+3y^2-40x-36y+158=0 ?
The solution to 5x^2+3y^2-40x-36y+158=0 is Ellipse with (h,k)=(4,6),a=sqrt(6),b=sqrt(10)