Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length of the horizontal chord of the parabola that has one end at (2/3, 1) .

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola:  

Part 1

If the curve passes through point , this means that when ,

Substitute these values into the equation and solve for :

Apply the exponent rule :

Part 2

We are told that one end of the chord is at and that the chord is horizontal.  Therefore, the y-coordinate of the other end of the chord will also be 1.  Substitute y = 1  into the equation for the parabola and solve for x:

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:  

**Please see attached diagram for drawn graph. Chord is in red**

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

answer: the answer is e

step-by-step explanation: