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dilip lalwani

Please solve these problems its urgent:

1)P(h,k) is a point on the circle x² + y²=a² .Find the locus of the midpoints of of all the chords having P as one extremity.

2)Find the equations of the locus of a point the tangents from which to the circle

x² + y²=a² include angle A.

I WON'T FORGET TO RATE.

rini s

one end of the chord is (h,k) itself and the other one will also be lying in the circle, there fore will be satisfying x²+y²=a².

now the mid point is {(h+m)/2 , (k+n)/2}.

where m and n are points on circle..

now,let mid point of chord=(x,y)

so,

x=(h+m)/2

=> m=2x-h-----------------(1)

and simillarly n=2y-k-----(2)

now, as m²+n²=a²

^{putting values frm (1) and(2),}

so, the locus is...

(2x-h)²+(2y-k)²=a²-------------solve and u'll get the required locus...

geethu

centre of cicle (0,0); radius =a

let (x,y) b d pt

distance bw centre & (x,y) =

(x²+y²)

angle bw 2 tgts = A

angle bw tgt & line joining (x,y) & centre = A/2

distance bw centre & (x,y) = a / sin(A/2)

ie

(x²+y²)= a / sin(A/2)

sin²(A/2) [x²+y²] = a^{2^]}

rini s

2)

the locus will be a consentric circle...

of radius = a/{sin(A/2)}

rini s

rate me!!!!

puneet

hey

good work done folks .. answers are already there ..
the solution by rini is short and precise and this is wat we look for .. in most cases .. so cheero to u ..

cheero

rini s

thankyou, sir!!

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