MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A curve is symmetric about the x-axis, has its vertex at the origin, and passes through the point (9,\,6). Answer the following questions.
(i) Sketch the curve by plotting the point (9,\,6) and using the given symmetry about the x-axis.
(ii) Show that the curve can be represented by an equation of the form y2=4ax and determine the value of a.
(iii) Using the equation obtained in part (ii), find the coordinates of the focus and write the equation of the directrix of the curve.
(iv) Find the points where the curve meets the x-axis and indicate these intercepts on your sketch.