Problems 1. , Find the standard form of the equation of a parabola opening to the right such that the endpoints of its latus rectum are the vertices of the hyperbola with the equation 9m2 + 4'92 541' + 16y = 101. 2. Find the values of integers a, b, and c that will make the ellipse 42:2 + 9'92 + at + by + c = 0 pass through the points (1, 1), (5, 1), and (2, 1). 3. Given the system of nonlinear inequalities 232+y24S0 {wyz+3>0 a. Solve algebraically for the point/s of intersection of the boundary curves. b_ Sketch the graph of the inequalities in the same coordinate plane and shade the solution region. Label the points obtained in part a