IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - parabola:problm from loney pls help........

ackhill

1)if a circle be drawn so as always to touch a given straight line and also a given circle,prove that the locus of its centre is parabola..

2)the verttex of a parabola is joined to any point P on the curve and PQ is drawn at right angles to AP to meet the axis at Q.prove that the projection of PQ on the axis is always equal to the LR.. ..

more problms r der but i`m trying those 2...but pls help me out with dese problms..pls..if u want rates i will do dat...

ackhill

sm1 help me fast!...u`ll must hv solved loney na??...pls help me guys....

ackhill

pls help!!!..smbody???....i will rate u as much as u want!!!..pls help!!!!

Conjurer

Can u tell me what are A, L and R in your second question. I am also trying the first question.

ackhill

ok..
A is the Vertex and LR means Latus Rectum....pls try na..

ackhill

smbody pls help!!!

ackhill

pls help...i cant even ask experts as i hv 0 nickels!!!!

bhartibhanushali

what is the equation of given circle

steps 1
write equation of first circle
2) since the circle touches line it must be tangent
let that point be (x1 ,y1)
3)it touches the other circle at certain point
let that point be (x2 , y2)
this point satisfies equation of both circle
(since u have not given a circle i cannot write the locus of that point)
its first equation

4)also we have centre of required circle as( -g,-f)
by distance formula u have another equation

solving these eqution u might get the locus of centre

nudge me if i m wrong

saurabh_reincarnated

see just analyze.......

wat is the defination of paraola.......

locus of points such that dist. frm a line and a point their ratio = 1

implies........ the dist. from a fixed line and frm a fixed point equal

see....

here the dist is r1+r2...... where r1 is of fixed circle so const...... but r2 is changing

here the fixed point is the centre of the fixed circle which is at dist. r1+r2 frm the moving circles centre

and fixed line the directrix is r1 distance away from the given line.... (the dist. of moving circle's centre is r2 frm the given line)

so dist of the line diretrix frm centre of moving circle is also r1+r2

hope u understand it...... just draw diagram

Cheers!!!

cursed_mask

go to Locus material on parabola you'll find all your doubts clarified there...here's the link:: go to the downloads section on this site::

www.locuseducation.org

Conjurer

These questions are definitely very good and require some thinking.I am revising my co-od now. So if i get to know the answer i will nudge u or something.

piit.jak

second question.

let the parabola be y2 = 4ax.

then vertex is (0,0).

let the point P be(at2,2at).

slope of PO is 2\t.

then slope of PQ is -t\2. (PQ perpendicular to OP)

equation of PQ is

(y-2at) = -t\2 (x-at2)

put y=0 to get the x coordinate of point Q.

It is x = at2-4a .

when PQ is projected along the x-axis then let the point where the point P touches the x-axis be called Z.

then x coordiante of Z is at2.

now to get the length of ZQ stract ehir respective x-coordinates.

YOU get

4a.

which is the length of the latus rectum.

hence proved.

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