What is a reciprocal? and how do I find for Parallel and Perpendicular line slopes?

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

Given f(x)=2x^2-8x+6 and g(x)=3x-1 find f(x) +g(x) a. 2x^2+5x+5 b.2x^2-11x+7 c. 2x^2-5x+5 d.2x^2-5x-5

Consider circle c with angle acb measuring 3/4 radians.if minor arc ab measures 9 inches, what is the length of the radius of circle c? if necessary, round your answer to the nearest inch.