What is 4x^2+y^2-16x+6y-75=0 ?

The solution to 4x^2+y^2-16x+6y-75=0 is Ellipse with (h,k)=(2,-3),a=5,b=10

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4x^2+y^2-16x+6y-75=0

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

(h, k) = (2, - 3), a = 5, b = 10

Solution steps

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

Rewrite

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 5, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = 10, a = 5

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 7 ) ^{2}}{49} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

What is 4x^2+y^2-16x+6y-75=0 ?
The solution to 4x^2+y^2-16x+6y-75=0 is Ellipse with (h,k)=(2,-3),a=5,b=10