Conic Sections For the hyperbola: x2 36 64 = 1 Find the explicit equation (where y is a function of x) for the hyperbola. Also find the two explicit equations for its asymptotes : b. Find the first quadrant y values of the hyperbola at : i. X = 0 : ii. X =4 : iii. x = 10 : iv. x = 20 : C. Find the general equation for the slope of the hyperbola at a point (x, y) : d. Find the first quadrant slopes of the hyperbola at the same points as in "b" above: i. X=0 : ii. x =4 : iii. x = 10 : iv. x = 20 :5. The function : sin x sinc x = X is important in a number of fields of analysis. a. Derive the first four terms of the Taylor series for this function, centered at approximately its first minimum for positive x (a = 4.49). b. Estimate the value of this function at a nearby x value (4.2) and compare your result to a value for sinc (4.42) determined by Excel or your calculator.6. Evaluate the limit using Taylor series: 3x2+ 8x - 4 sin 2x lim x2