MODERATE EXERCISES - Circles and other Conic Sections
(1) Find an equation that represents a hyperbola on which the closest points to the origin are (-4,0) and (4,0) and which has asymptotic lines y = 3x and y = -3x.
(2) There are important functions whose graphs are a part of some conic. For example, the graph of the square root function, s(x) = , is the upper half of the parabola represented by the equation y2 = x. For each of these functions, find their domain, describe which part of what conic gives their graph and sketch their graph.
(b) g(x)= 3 -
(c) h(x) =
(d) F(x) =
(3) Describe the solution curve represented by each of the following equations and sketch the graph:
(a) x2 + y2 - 4x - 6y + 13 = 0
(b) y2 + 4y + 2 = x2 + 2x
(c) y2 - 5y + 3 = 2x + (y - 3)2
(4) Find the equation of each circle described below:
(a) center at the origin and passing through (4,7)
(b) center at (3,-2) and has y-intercept at -1.
(c) endpoints of a diameter are (-2,3) and (3,-1).
(d) center at (3,5) and tangent to the x-axis.
(5) Sketch the following systems and find any real solutions:
(a) x2 + y2 = 25 and x2 - y2 = 7
(b) 16x2 + 9y2 = 144 and y = x2 + 5