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Chords Equidistant from Center Are Equal

29. Two equal...

Question

29. Two equal chords AB and AC of the circle x^2+ y^2- 6x-8y -24= 0 are drawn from the point A(V33 +3,0).Another chord PQ is drawn intersecting AB and AC at points R and S, respectively given that AR=SC =7 and RB =AS 3. The value of PR/QS is(a) 1(c) 2(d) None of these

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A B

A C

r

A B = 2 A C

P

Q

A B

A C

4 q^{2} = p^{2} + 3 r^{2}

P (- 1, - 2)

P Q

P R

x^{2} + y^{2} - 6 x - 8 y = 0

Q R

x^{2} + 4 x + (y - 3)^{2} = 0

From origin, chords are drawn to the circle $x^{2} + y^{2} - 2 y = 0$ .The locus of the middle points of these chords is

(2, 2)

x^{2} + y^{2} - 2 x - 4 y + 1 = 0

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