Loci and Their Equations

Covers the concept of a locus, the three-step method for finding the equation of a locus, and several worked loci based on distance conditions.

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Views #: 125
Questions #: 11
Time: 20 minutes
Pass Score: 80.0%
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Defining a Locus

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The set of points in a plane satisfying a given geometric condition is called a ______.
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The Locus of Points at a Fixed Distance

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crP

Locus of points at fixed distance r from a fixed point c

The locus of points in a plane that are all at the same distance \( r \) from a fixed point \( c \) is a:

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The Locus of Points Equidistant From Two Fixed Points

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ABP

Locus of points equidistant from A and B

The locus of points equidistant from two fixed points A and B is the:

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Order the Steps to Find a Locus Equation

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Arrange the three steps of the standard method for obtaining the equation of a locus in the correct order.
Replace x' by x and y' by y to get the required equation
Take any point P(x', y') of the locus
Express the geometric condition as a relation between x' and y'
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Locus: Abscissa Exceeds Twice the Ordinate by 7

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Find the equation of the locus of P(x, y) if the abscissa of P exceeds twice its ordinate by 7.
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Locus: Sum of Coordinates is 11

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Find the equation of the locus of P(x, y) if the sum of its coordinates is 11.
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Locus: Sum of Squared Distances From the Axes

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Find the equation of the locus of P(x, y) if the sum of the squares of its distances from the coordinate axes is 9.
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Locus: Sum of Squared Distances From Two Points

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A point P(x, y) moves so that the sum of the squares of its distances from A(0, 0) and B(2, −4) is always 20. The equation of the locus is \(x^2+y^2\) − (1) x + (2) y = 0.

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2
4
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Locus: Equidistant From the y-axis and a Point

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A point moves so that its distance from the y-axis is always equal to its distance from the fixed point A(4, 0). Find the equation of this locus.
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Length of a Chord on the x-axis

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The curve \(x^2+y^2+5x+4=0\) crosses the x-axis at two points. What is the length of the intercept (chord) it makes on the x-axis?

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A Locus Need Not Be an Equation

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The region x² + y² < 1 (inside the unit circle)

True or False: A locus can be represented by an inequality rather than an equation.

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0
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sin-1 cos-1 tan-1 π e
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y√x 3√x √x ln log
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7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC
Keywords
Year 12 Year 11