The locus of centres of circles which touch a given line at a given point is a

parabola

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straight line

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circle

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None of these

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Solution

The correct option is B straight line
As $O P, O^{'} P, O " P$ are the radii of the circles touching line $T$ at $P$ ,
it is perpendicular to the given line.
So $O P, O^{'} P, O " P$ represent the same straight line.
Hence the required locus is a straight line.

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Similar questions

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

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