y x 3 2 1 1 4 1 1 4 Read the coordinates of the points of intersection from the

# Y x 3 2 1 1 4 1 1 4 read the coordinates of the

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(4) Read the coordinates of the points of intersection from the graph. The common solutions are ( 1, 4) and (2, 1). Answer ( 1, 4) and (2, 1) or x 1, y 4 and x 2, y 1 Writing About Mathematics 1.Luis said that the solutions to the equation x22x8 0 are the x-coordinates of thepoints at which the graph of y x22x8 intersects the y-axis. Do you agree withLuis? Explain why or why not.2.Amanda said that if the turning point of a parabola is (1, 0), then the x-axis is tangent to theparabola. Do you agree with Amanda? Explain why or why not.Developing SkillsIn 38, find the coordinates of the turning point and the equation of the axis of symmetry of eachparabola.3.yx26x 14.yx22x 35.yx24x 6.yx22x 57.yx28x 48.yx25x In 916, find the common solution of each system of equations graphically and check your solution.9.yx22x 210.yx2y x2xy 11.yx24x 312.yx22x y x1y 1 13.yx24x 214.yx22x y 2x3y 2x15.yx26x 516.y2x xy 7 2xy 2In 1720 write the equation of the parabola that is the locus of points equidistant from each givenpoint and line. 1 2 1 1 3 x 2 2 2 x 4 17. and 18. and 19. F (0, 2) and y 2 20. F (3, 3) and y 3 y 5 1 4 F A 0, 2 1 4 B y 5 2 1 4 F A 0, 1 4 B Exercises Points Equidistant from a Point and a Line 629
Hands-On ActivityIf the graph of an equation is moved hunits in the horizontal direction and kunits in the verticaldirection, then xis replaced by x hand yis replaced by y kin the given equation.1.The turning point of the parabola y ax2is (0, 0). If the parabola yax2is moved so thatthe coordinates of the turning point are (3, 5), what is the equation of the parabola?2.If the parabola yax2is moved so that the coordinates of the turning point are (h,k), whatis the equation of the parabola? CHAPTER SUMMARY • A locus of points is the set of all points, and only those points, that satisfy a given condition. • The locus of points equidistant from two fixed points that are the end- points of a segment is the perpendicular bisector of the segment. • The locus of points equidistant from two intersecting lines is a pair of lines that bisect the angles formed by the intersecting lines. • The locus of points equidistant from two parallel lines is a third line, paral- lel to the given lines and midway between them. • The locus of points at a fixed distance from a line is a pair of lines, each parallel to the given line and at the fixed distance from the given line. • The locus of points at a fixed distance from a fixed point is a circle whose center is the fixed point and whose radius is the fixed distance. • The locus of points equidistant from a fixed point and a line is a parabola. • The locus of points in the coordinate plane r units from ( h , k ) is the circle whose equation is ( x h ) 2 ( y k ) 2 r 2 . • The locus of points d units from the horizontal line y a is the pair of lines y a d and y a d . • The locus of points d units from the vertical line x a is the pair of lines x a d and x a d . • The locus of points equidistant from A ( a , c ) and B ( b , d
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