What is 10x^2+y^2-40x=0 ?

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

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10x^2+y^2-40x=0

10 x^{2} + y^{2} - 40 x = 0

(h, k) = (2, 0), a = 2, b = 210

Solution steps

10 x^{2} + y^{2} - 40 x = 0

Rewrite

10 x^{2} + y^{2} - 40 x = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), a = 2, b = 210

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 0), b = 210, a = 2

4 x^{2} + 16 x + 16 y^{2} - 32 y - 32 = 0

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 7 )} = 1

\frac{( x - 4 ) ^{2}}{5 ^{2}} + \frac{( y - 7 ) ^{2}}{3 ^{2}} = 1

9 x^{2} + 25 y^{2} + 18 x - 50 y = 191

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

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