Here are some conic questions that am having problems with :

1) The general form of a particular ellipse is show Below. If the conic is translated 2 units left and 1 unit down, determine the new general term.

2x^{2}+y^{2}-2x+3y-9=0

2) Find the equation of a hyperbola in standard form or general form, that has its centre at (-2, 5), one vertex at (-2, 10), and the slope of one of its asymptotes is 5/4 .

There is no need to convert to standard form. "Translating 2 units left" is exactly the same as adding 2 to x. "Translating one unit down" is exactly the same as subtracting 1 from y. Replace x by x+2 and y by y- 1.

Rotating through an angle [itex]\theta[/itex] gives [itex]x'= x cos(\theta)+ y sin(\theta)[/itex], [itex]y'= x sin(\theta)- y cos(\theta)[/itex]. Replace x by [itex]x cos(\theta)+ y sin(\theta)[/itex], y by [itex]x sin(\theta)- y cos(\theta)[/itex]. [itex]\theta= arctan(5/4)[/itex].