The parabola P has focus (0,0) and goes through the points (4,3) and (−4,−3). For how many points (x,y)∈P with integer coefficients is it true that ∣4x+3y∣≤1000?<spanclass=′latex−bold′>(A)</span>38<spanclass=′latex−bold′>(B)</span>40<spanclass=′latex−bold′>(C)</span>42<spanclass=′latex−bold′>(D)</span>44<spanclass=′latex−bold′>(E)</span>46