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Question

Find the equation of the parabola with the vertex at (4,5) and directrix at x=6.

Solve for x on the interval [0,2pi]: sinx-sin2s=0

Please help me with either one or both.
Thanks

Answer 1

The equation for a parabola with vertex at (h,k) and directrix x=p Is

(y - k)^2 = 4p(x - h)^2

Plug in your values and multiply out.

I presume your second equation is sinx - sin2x = 0. Use the identity sin2A = (2sinA)(cosA) to get

sinx - 2(sinx)(cosx) = 0

1 - 2cosx = 0,

cosx = 1/2

In the range 0 to 2π there will be two angles x that satisfy that equation

x = π/3 and x=5*π/3