What is 21y^2+210y+25x^2-100x=0 ?

The solution to 21y^2+210y+25x^2-100x=0 is Ellipse with (h,k)=(2,-5),a=5,b=(25)/(sqrt(21))

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21y^2+210y+25x^2-100x=0

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

(h, k) = (2, - 5), a = 5, b = \frac{25}{21}

Solution steps

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

Rewrite

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( \frac{25}{21} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 5), a = 5, b = \frac{25}{21}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 5), b = \frac{25}{21}, a = 5

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

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

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

36 (x^{2} - x) + 64 (y^{2} + 4 y) + 256 = 576

What is 21y^2+210y+25x^2-100x=0 ?
The solution to 21y^2+210y+25x^2-100x=0 is Ellipse with (h,k)=(2,-5),a=5,b=(25)/(sqrt(21))