What is 2x^2-8x+y^2-10y=60 ?

The solution to 2x^2-8x+y^2-10y=60 is Ellipse with (h,k)=(2,5),a=sqrt(93/2),b=sqrt(93)

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2x^2-8x+y^2-10y=60

2 x^{2} - 8 x + y^{2} - 10 y = 60

(h, k) = (2, 5), a = \frac{93}{2}, b = 93

Solution steps

2 x^{2} - 8 x + y^{2} - 10 y = 60

Rewrite

2 x^{2} - 8 x + y^{2} - 10 y = 60

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{93}{2} ) ^{2}} + \frac{( y - 5 ) ^{2}}{( 93 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 5), a = \frac{93}{2}, b = 93

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 5), b = 93, a = \frac{93}{2}

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

2 x^{2} + 2 y^{2} - 36 y = 0

\frac{x ^{2}}{8 0 ^{2}} + \frac{y ^{2}}{62. 5 ^{2}} = 1

4 y^{2} + z^{2} = 4

9 y^{2} + 16 x^{2} = 144

What is 2x^2-8x+y^2-10y=60 ?
The solution to 2x^2-8x+y^2-10y=60 is Ellipse with (h,k)=(2,5),a=sqrt(93/2),b=sqrt(93)