Call the point where BK intersects AM point X. BX is the altitude of ∆ABM, and it is also the angle bisector of angle ∠ABM. Hence ∆ABM is isosceles, and AB ≅ MB.
M is the midpoint of BC, which is 12 inches long. Hence MB is half that length, or 6 inches.
Since AB is the same length as MB, which is 6 inches, ...
... AB is 6 inches.
Answer:
The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is .
Step-by-step explanation:
As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:
Where:
,
- Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.
- Least distance of directrix with respect to vertex, dimensionless.
Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:
Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is .
For this case we have the following system of equations:
We solve by the substitution method:
We substitute the first equation in the second equation:
We apply distributive property considering that
We subtract 69 from both sides of the equation:
We divide by 8 on both sides of the equation:
We look for the value of the variable y:
Thus, the solution of the system is
Answer: