What is 4x^2+5y^2-32x+30y-11=0 ?

The solution to 4x^2+5y^2-32x+30y-11=0 is Ellipse with (h,k)=(4,-3),a=sqrt(30),b=2sqrt(6)

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4x^2+5y^2-32x+30y-11=0

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

(h, k) = (4, - 3), a = 30, b = 26

Solution steps

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

Rewrite

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 30 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 2 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 3), a = 30, b = 26

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 3), a = 30, b = 26

\frac{( x - 4 ) ^{2}}{100} + \frac{( y + 5 ) ^{2}}{49} = 1

5 y^{2} + z^{2} = 36

2 x^{(2)} + y^{(2)} = 1

16 - x^{2} - 9 y^{2} = - 1

y^{2} = 100 - 4 x^{2}

What is 4x^2+5y^2-32x+30y-11=0 ?
The solution to 4x^2+5y^2-32x+30y-11=0 is Ellipse with (h,k)=(4,-3),a=sqrt(30),b=2sqrt(6)