Quandaries
and Queries 

Dear Math Expert I am a maths tutor. One of my year 12 students has given me this assignment. Many parts are ambiguous. I am trying to determine the equation of the line segment AB. Given that A has an incline of 10 degrees below the horizontal, I am assuming that this parabola (although you can only see part of it) has been rotated 10 degree clockwise. Am I right in assuming this? If so, how do I derive the equation of the parabola as it will then not fit the general form y = ax squared +bx +c of a parabola. Also, how is one expected to find the x coordinate of D without the equation of this parabola. To find the equation you need the xcoordinate and therefore be able to find another point on the parabola in order to derive the equation using simultaneous equations. I am just blown away. Please help. 

Hi, I labeled the diagram you sent with the given information, introducing variables where I needed them.
The main part of the text you sent is In your question you asked "Given that A has an incline of 10 degrees below the horizontal, I am assuming that this parabola (although you can only see part of it) has been rotated 10 degree clockwise. Am I right in assuming this?" As you can see from the way I labeled the diagram, I assumed that the parabola that contains the segment AB has its vertex above and to the left of A at (p,q), and hence has equation
Since this parabola passes through A and B
The slope of the tangent to this parabola at (0,30) is tan(10^{o}) so
These three equations are enough to determine a, p and q, and thus the equation of the parabola. Can you complete the problem now? Penny 

