Flag Analytical Geometry> parabola...
question mark

If a circle is drawn so as always to touch a given straight line and also a given circle externally then prove that the locus of its centre is a parabola.(given line and given circle are non intersecting)

vineet kumar , 13 Years ago
Grade Upto college level
anser 2 Answers
Chetan Mandayam Nayakar

Last Activity: 13 Years ago

let O be centre of given circle, P be the centre of the circle whose locus is to be found, Q be the point of contact of the two circles, and PR be perpendicular to the given line.

PQ=PR, PQ+OQ=PR+OQ

thus the locus of P is such that its distance from a point O is equal to its perpendicular distance from a line( which is situated at a distance OQ from the given line, on the other side of the given circle). This description of the locus of P exactly fits the definition of a parabola.

Varun mishra

Last Activity: 7 Years ago

Take any circle with centre O with centre r1 and P be the centre of circle (radius r) whose locus is to be found. Draw perpendicular to the given line say it is PM. Now produce PM to R such that PO is equal to PR.Now as PO is equal to PR , by classical definition of Parabola , Perpendicular Distance=Distance from fixed Pt.We may say that the locus of P is a Parabola

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...