Question

1.Find the locus of centres of circles which touch a given line at a given point.

2. Find the locus of centres of circles which touch two intersecting lines.

Help me plzzz...... FAST

Answer 1

... Thus the difference of the distances to the circles' centers is constant. The locus is therefore part of a hyperbola having the centers of the circles as focii. In fact, it is subarcs of a branch on this hyperbola.

Of course, points

P

i

Pi

are points of these subarcs.

for 2nd ques

Answer 2

ANSWER:

Given: Circles with centres O,O',O" touching line T at P.

To prove : To find the locus of centres of circles which touch a given line at a given point.



Proof: As OP,O'P,O"P are the radii of the circles touching line T at P, it is

perpendicular to the given line.

∴ OP,O'P,O"P represent the same straight line passing through P and ⟂ to PT.

Hence the locus of the centres of circles which touch a given a line at a given

point is a straight line to the given line at the given point.