What is 5x^2+9y^2-30x=0 ?

The solution to 5x^2+9y^2-30x=0 is Ellipse with (h,k)=(3,0),a=3,b=sqrt(5)

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5x^2+9y^2-30x=0

5 x^{2} + 9 y^{2} - 30 x = 0

(h, k) = (3, 0), a = 3, b = 5

Solution steps

5 x^{2} + 9 y^{2} - 30 x = 0

Rewrite

5 x^{2} + 9 y^{2} - 30 x = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 0), a = 3, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 0), a = 3, b = 5

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

2 a^{2} + b^{2} = a + b

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

x^{2} + 3 (y^{2}) = 84

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

What is 5x^2+9y^2-30x=0 ?
The solution to 5x^2+9y^2-30x=0 is Ellipse with (h,k)=(3,0),a=3,b=sqrt(5)