Review-Final - Review for final exam of Math 201 Jing Zhang Useful formulas and methods 1(1 Distance Formulas The distance between any two points P(x1

# Review-Final - Review for final exam of Math 201 Jing Zhang...

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Review for final exam of Math 201 Jing Zhang November 19, 2014 Useful formulas and methods 1. (1)Distance FormulasThe distance between any two pointsP(x1, y1) andQ(x2, y2) in the coordinate plane, denotedd(P, Q), isd(P, Q) =p(x2-x1)2+ (y2-y1)2(2)Midpoint FormulaThe coordinates of the midpointM(x, y) on the line segment joiningP(x1, y1) andQ(x2, y2)are given byM(x, y) = (x1+x22,y1+y22)2. (1) 1
3. (1) Parallel Lines: Two nonvertical lines are parallel if and only if they have the same slope . (2) Perpendicular Lines: Two lines with slopes m 1 and m 2 are perpendicular if and only if m 1 m 2 = - 1,that is, their slopes are negative reciprocals : m 2 = - 1 m 1 (3) Finding Equations of Parallel and Perpendicular Lines: Let a line l : Ax + By + C = 0. Find the equation of each line through the point ( x 1 , y 1 ): (a) l 1 parallel to l ; (b) l 2 perpendicular to l . Step 1 Find the slope m of l . Write l in the form y = mx + b . Step 2 Write slope of l 1 and l 2 . The slope m 1 of l 1 is m . The slope m 2 of l 2 is - 1 m . Step 3 Write equation of l 1 and l 2 . Use point-slope form to write equations of l 1 and l 1 . Simplify to write equations in the requested form. 4. Equation of a circle: (1) The standard form for the equation of a circle with center ( h, k ) and radius r is ( x - h ) 2 + ( y - k ) 2 = r 2 (2) If you are given the equation of a circle in general form. Then to find its center and radius, you must put the equation back in standard form. To do this, you need to complete the square for all the x and y -terms. To make x 2 + bx a perfect square, add ( 1 2 b ) 2 to get x 2 + bx + ( 1 2 b ) 2 = ( x + 1 2 b ) 2 5. Rational Functions; (1) x - intercepts: In order to find the x - intercepts, you just set y = 0 and solve for x . For the rational function: y = 0 equivalent to the numerator equals to 0. 2