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Problem 679

Write an equation of the locus of points equidistant from the points \(\mathrm{P}_{1}(2,2)\) and \(\mathrm{P}_{2}(6,2)\).

Expert verified

The equation of the locus of points equidistant from the points \(\mathrm{P}_{1}(2,2)\) and \(\mathrm{P}_{2}(6,2)\) is \(x=4\).

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Chapter 39

Write an equation for the locus of points equidistant from \((3,3)\) and \((4,4)\).

Chapter 39

(a) Write an equation of the locus of points whose distance from the origin is \(5 .\) (b) Determine whether the point \((-3,4)\) is on the locus.

Chapter 39

What is the locus of points traced by the center of a circle with radius \(\mathrm{R}_{2}\) that rolls around a second circle, the radius of which is \(R_{1}\) ?

Chapter 39

Prove that the locus of points equidistant from the ends of a given line segment is the perpendicular bisector of the line segment. Prove the converse of this statement.

Chapter 39

(a) Describe the locus of points 2 units from the y-axis and write an equation of this locus, (b) Describe the locus of points equidistant from the points \(\mathrm{P}_{1}(-4,2)\) and \(\mathrm{P}_{2}(-4,6)\) and write an equation for this locus. (c) Find the number of points which satisfy both conditions stated in (a) and (b) and give the coordinates of each point.

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