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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 ( ) , h k : ( ) ( ) 2 2 2 x h y k r + = Distance on the plane between points ( ) 1 1 , x y and ( ) 2 2 , x y : ( ) ( ) 2 2 2 1 2 1 d x x y y = + Midpoint Formula: 1 2 1 2 , 2 2 x x y y M + + = The slope of the line through ( ) 1 1 , x y and ( ) 2 2 , x y : 2 1 2 1 y y y m x x x = = . Equation of the line with slope m through the point ( ) 1 1 , x y : ( ) 1 1 y y m x x = . Equation of the line with x and y intercepts a and b : 1 x y a b + = ( 0, 0 a b ) Average rate of change of f on the interval [ ] , c x is ( ) ( ) f x f c x c ( x c ). Vertex of the parabola 2 ( ) f x ax bx c = + + is ( ) , h k , where 2 b h a = , ( ) k f h = . Properties of Exponents ( 0, 1, 0, 1) a a b b > > : x y x y a a a + = x x y y a a a = ( ) y x x y a a = 1 x x a a = 0 1 a = ( ) x x x ab a b = x x x a a b b = Identities: log a x a x = ( 0 x > ), log x a a x = ( x is any real number) 1. Given points ( 3,5) P and (3, 2) Q . (a) Find ( , ) d P Q (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 2 2 3 3 12 6 1 0 x y x y + + = .
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