What is 25x^2+36y^2-350x+350=0 ?

The solution to 25x^2+36y^2-350x+350=0 is Ellipse with (h,k)=(7,0),a=sqrt(35),b=(5sqrt(35))/6

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25x^2+36y^2-350x+350=0

25 x^{2} + 36 y^{2} - 350 x + 350 = 0

(h, k) = (7, 0), a = 35, b = \frac{5 35}{6}

Solution steps

25 x^{2} + 36 y^{2} - 350 x + 350 = 0

Rewrite

25 x^{2} + 36 y^{2} - 350 x + 350 = 0

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{( 35 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5 35}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, 0), a = 35, b = \frac{5 35}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, 0), a = 35, b = \frac{5 35}{6}

4 (x - 4)^{2} + 9 (y + 5)^{2} = 36

15 x^{2} + 15 y^{2} + 16 y \geq 0

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

4 - 4 x^{2} - y^{2} \geq 0

x^{2} + 5 y^{2} = 20

What is 25x^2+36y^2-350x+350=0 ?
The solution to 25x^2+36y^2-350x+350=0 is Ellipse with (h,k)=(7,0),a=sqrt(35),b=(5sqrt(35))/6