Two circles are S 1 ≡ (x + 3) 2 + y 2 = 9
S 2 ≡ (x – 5) 2 + y 2 = 16
with centres C 1 & C 2
S 1 ≡ (x + 3) 2 + y 2 = 9
S 2 ≡ (x – 5) 2 + y 2 = 16
(i) A direct common tangent is drawn from a point P (on x-axis) which touches S 1 & S 2 at Q & R, respectively. Find the ratio of area of Δ PQC 1 & Δ PRC 2 .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) Δ PQC 1 and Δ PRC 2 are similar
= 
= 
(ii) . Let mid point m(h, k). Now equation of chord
T = S 1
hx + ky + 3(x + h) = h 2 + k 2 + 6h
it passes through (1, 0)
h + 3(1 + h) = h 2 + k 2 + 6h
locus x 2 + y 2 + 2x – 3 = 0
But clear from Geometry it will be arc of BC
(iii) Common chord of S 1 & answer of 5
4x + 3 = 0 ⇒ x = –3/4
at x = –3/4 
+ y 2 = 9 ⇒ y 2 = 9 – 
y 2 = 
⇒ y = ± 
Hence tan θ = 
= 
⇒ tan θ = 
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