mac1147_review_2 - REVIEW UNIT II MAC1147 FORMULAS TO...

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1 REVIEW UNIT II MAC1147 FORMULAS TO MEMORIZE : Equation of a circle with radius r and center ( ) , hk : () 22 2 x hy k r +− = Distance on the plane between points ( ) 11 , x y and ( ) , x y : 21 dx x y y =− + Midpoint Formula: 12 , x xy y M ++ ⎛⎞ = ⎜⎟ ⎝⎠ The slope of the line through ( ) , x y and ( ) , x y : yy y m x xx == . Equation of the line with slope m through the point ( ) , x y : ( ) yy m . Equation of the line with x and y intercepts a and b : 1 x y ab + = ( 0, 0 ≠≠ ) Average rate of change of f on the interval [ ] , cx is ( ) ( ) f xf c xc ( x c ). Vertex of the parabola 2 f xa xb x c =+ + is ( ) , , where 2 b h a = , kf h = . Properties of Exponents (0 , 1 , 0 ,1 ) aa b b >≠ > : x yx y aa a + ⋅= x x y y a a a = ( ) y x xy = 1 x x a a = 0 1 a = ( ) x x x ab a b =⋅ x x x bb = Identities: log a x ax = ( 0 x > ), log x a = ( x is any real number) 1. Given points (3 , 5 ) P and (3, 2) Q . (a) Find (,) dPQ (b) Find the midpoint of the segment joining the two points. (c) Determine whether the point (69, 79) is on the line passing through the points P and Q . 2. Find the equation of the circle with center ( ) 5, 3 passing through the point 1, 0 . 3. Find the center-radius equation of a circle if the endpoints of the diameter are 1, 2 and ( ) 9,6 . 4. Complete the square to find center and radius of the circle 331 2 6 1 0 x y ++− = . 5. Write the equation of the line passing through point (6 ,3 ) and parallel to the line through ( ) and 1 2 (,4 ) . Give the final answer in a standard form.
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mac1147_review_2 - REVIEW UNIT II MAC1147 FORMULAS TO...

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