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Unformatted text preview: Circle : Circle midpoint-1 distance-2 line equation -3 slope -4 intersection of two lines -5 circle equation-6 completing the square -7 instructions of a circle and line -8 trigonometry -9 midpoint : X 1 + X 2 Y 1 +Y 2 , 2 2 : Find the midpoint B = (1,3) A = ( 3,5 ) : A = ( 3,5 ) A = ( X 1, y 1) B = ( 1,3) B = ( X 2, y 2 ) x1 ,x2,y1,y2 3 +1 5 + 3 = , ( 2, 4 ) 2 2 distance : = ( X 1 - X 2) 2 + (Y 1 -Y 2 ) 2 : Find the distance B = (1,3) A = ( 3,5 ) = ( 3 - 1) 2 + ( 5 - 3) = 4 + 4 = 8 2 slope : : Slope y = mx + c ( equation ) m= y 1- y (points 2 ) x 1- x -1 -2 : A=(-1,2) B=(1,10 (AB ) . : m= 2 -1 1 = -1 - 1 -2 1 : 2x + 3 y + 4 = 0 : = : y y = mx + c y 3 y = -2x - 4 -2 4 y = x- 3 3 X -2 = 3 line equation : : line equation y = mx + c ( y (slope +y-intercept (m) 1 y - y 1 = m (x - x 1) ( point) ( slope) 2 : (2points) 3 - 2 : : 1 -1 = 2 y =-5 : y = mx + c y = -1 x -5 2 :2 (-1, 2) 2 3 : : y - y 1 = m (x - x 1) y -2= y = 2 (x + 1) 3 2 2 x + ( + 2) 3 3 :3 : A = (-2,3) B = (1, 2) : : m= y 1- y : x 1- x 3- 2 -2 - 1 1 m= -3 m= y - y 1 = m (x - x 1) : -1 ( x - 1) 3 -1 1 y = x + ( + 2) 3 3 y -2= : intersection of two lines : (= ) intersection of two lines : y = m 1x + c1 : y = m 2x + c 2 : intersection of two lines : m 1x + c1 = m 2x + c 2 m 1x - m 2x = c 2 - c1 x (m 1 - m 2) = c 2 - c 1 c 2 - c1 x = m1 - m 2 x c 2 - c1 y = m 1 + c1 m 1- m 2 circle equation : : (x - a ) 2 + ( y - b ) 2 = r 2 : a,b) = center) ( R= (radius : Write down the equation of the circle in the center (-3,1) and radius is 2 : (x - a ) 2 + ( y - b ) 2 = r 2 (x - (-3)) 2 + ( y - 1) 2 = 22 (x + 3) 2 + ( y - 1) 2 = 22 x 2 + 9 + y 2 + 1 = +4 x 2 + y 2 = -9 - 1 + 4 x 2 + y 2 = -6 com pleting the square : A X 2 + aX A a a X + aX X + aX + - 2 2 2 2 2 2 a a a a X + aX X + aX + - + - x 2 2 2 2 2 2 2 2 2 2 X 2 - 10X = 1 2 X 2 - 10X = 1 X 2 - 10X + (5) 2 - (5) 2 = 1 ( X - 5 ) = 1 + 25 : instructions of a circle and line -8 trigonometry -9 ...
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