What is 2x^2-80x+y^2+49=0(0) ?

The solution to 2x^2-80x+y^2+49=0(0) is Ellipse with (h,k)=(20,0),a=sqrt(751/2),b=sqrt(751)

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2x^2-80x+y^2+49=0(0)

2 x^{2} - 80 x + y^{2} + 49 = 0 (0)

(h, k) = (20, 0), a = \frac{751}{2}, b = 751

Solution steps

2 x^{2} - 80 x + y^{2} + 49 = 0 \cdot 0

Rewrite

2 x^{2} - 80 x + y^{2} + 49 = 00

in the form of the standard ellipse equation

\frac{( x - 20 ) ^{2}}{( \frac{751}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 751 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (20, 0), a = \frac{751}{2}, b = 751

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (20, 0), b = 751, a = \frac{751}{2}

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(x, x^{5}) \to (0, 0) lim (\frac{x ^{5} y}{x ^{10} + y ^{5}})

x \to 2 - lim (\frac{6 x}{x - 2})

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What is 2x^2-80x+y^2+49=0(0) ?
The solution to 2x^2-80x+y^2+49=0(0) is Ellipse with (h,k)=(20,0),a=sqrt(751/2),b=sqrt(751)