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Sequences And Series

Question
CBSEENMA11014986
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Find the equation of the locus of a point P or the equation of set of points P which moves so that its distance from A (1, 2, 3) is four times its distance from the YZ-plane.

Solution

Let point P be (x, y, z) and A (1, 2, 3) be the given point. The given condition for locus is:
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Squaring both sides, we get
                 space space left parenthesis straight x minus 1 right parenthesis squared plus left parenthesis straight y minus 2 right parenthesis squared plus left parenthesis straight z minus 3 right parenthesis squared space equals space 16 straight x squared
Hence, locus of P is 15 straight x squared minus straight y squared minus straight z squared plus 2 straight x plus 4 straight y plus 6 straight z minus 14 equals 0

Some More Questions From Sequences and Series Chapter

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

A point lies on the x-axis at a distance of 5 units towards OX'. What are its co-ordinates?

A point lies on z-axis at a distance of 3 units in the direction OZ. Write its co-ordinates.

A point lies on y-axis and is at a distance of 4 units in the direction OY'. Write its co-ordinates.

A point lies on XY-plane with distances 4 units along OX and 3 units along OY. Write its co-ordinates.

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