Show that the equations of the parabola and hyperbola with vertex (a, 0) and focus (c, 0),

Question:

Show that the equations of the parabola and hyperbola with vertex (a, 0) and focus (c, 0), c > a > 0, can be written as as = y2 = 4(c - a) (x - a) and y2 = (b2/a2) (x2 - a2), respectively. Then use these expressions for y2 to show that the parabola is al-ways Inside" the right branch of the hyperbola.