Let C be a circle and L be a line on the same plane such that C and L do not intersect. Let P be a moving...?

point such that the circle drawn with center at P to touch L also touches C. Then the locus of P is,


A) a straight line parallel to L not intersecting C;


B) a circle concentric with C;


C) a parabola whose focus is the center of C and whose directrix is L;


D) a parabola whose focus is the center of C and whose directrix is a straight line parallel to L;


Kindly explain your answer...

Let C be a circle and L be a line on the same plane such that C and L do not intersect. Let P be a moving...?
Sketch a line and circle on a bit of paper, and a couple of easy possibilities for a point P, to see that options A %26amp; B are not right.





Consider the definition of a parabola - given any focus point F and directrix line G (not touching F), the parabola is the locus of points equidistant from F and G (the distance from G being perpendicular).





Consider each possible point P - the difference between the distance from P to C, and from P to L (perpendicularly) will always be different by the same amount - the radius of C.





So the answer can't be C since P will always be further from C than L, by a distance the same as the radius of C.





So the answer must be D.

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