Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4.

Step-by-step explanation:

Equation of the Parabola

The standard form of the parabola with the axis of symmetry parallel to the y-axis, vertex at (h.k) and directrix y=k-p is

If the parabola has its axis of symmetry parallel to the x-axis, vertex at (h.k) and directrix x=h-p is

The focus of this form of the parabola is located at (h+p,k)

The parabola described in the question belongs to the second form since the directrix is at x=4. We also know that the focus is at (-4,0). We can find the values of h and p by equating

Adding up both  equations

then

The vertex is (h,k)=(0,0)

We can now write the equation of the parabola as

Simplifying

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq