What is (y-2)^2=(x-1)^2+(y+4)^2 ?

The solution to (y-2)^2=(x-1)^2+(y+4)^2 is Parabola with (h,k)=(1,0),p=-3

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(y-2)^2=(x-1)^2+(y+4)^2

(y - 2)^{2} = (x - 1)^{2} + (y + 4)^{2}

(h, k) = (1, 0), p = - 3

Solution steps

(y - 2)^{2} = (x - 1)^{2} + (y + 4)^{2}

Rewrite

(y - 2)^{2} = (x - 1)^{2} + (y + 4)^{2}

in the standard form

4 (- 3) (y - 0) = (x - 1)^{2}

Therefore parabola properties are:

(h, k) = (1, 0), p = - 3

x^{2} + 2 x + y^{2} = 8

\frac{y ^{2}}{16} - \frac{x ^{2}}{9} = 1

4 x^{2} - 9 y^{2} = 36

9 y^{2} - 4 x^{2} = 36

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

What is (y-2)^2=(x-1)^2+(y+4)^2 ?
The solution to (y-2)^2=(x-1)^2+(y+4)^2 is Parabola with (h,k)=(1,0),p=-3