What is the foci y=((-6(r+4r^2)+9r^2+6r)^2)/(9r^2) ?

The foci y=((-6(r+4r^2)+9r^2+6r)^2)/(9r^2) is (1/100 ,0)

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foci y=((-6(r+4r^2)+9r^2+6r)^2)/(9r^2)

foci

y = \frac{( - 6 ( r + 4 r ^{2} ) + 9 r ^{2} + 6 r ) ^{2}}{9 r ^{2}}

(\frac{1}{100}, 0)

Solution steps

Rewrite

y = \frac{( - 6 ( r + 4 r ^{2} ) + 9 r ^{2} + 6 r ) ^{2}}{9 r ^{2}}

in the standard form

4 \cdot \frac{1}{100} (y - 0) = (r - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{100}

Parabola is symmetric around the x-axis and so the focus lies a distance

p

from the center

(0, 0)

along the x-axis

(0 + p, 0)

= (0 + \frac{1}{100}, 0)

Refine

(\frac{1}{100}, 0)

y^{2} + 2 y - 4 x + 9 = 0

(x - 5) (x + 2)

(x + 1)^{2} + 3

y^{2} + 2 y + 12 x + 25 = 0

(x - 3)^{2} = y - 7

What is the foci y=((-6(r+4r^2)+9r^2+6r)^2)/(9r^2) ?
The foci y=((-6(r+4r^2)+9r^2+6r)^2)/(9r^2) is (1/100 ,0)