A ball moving around the circle x² + y² − 2x − 4y − 20 = 0 in anti − clockwise direction leaves it tangentially at the point P( − 2, − 2). After getting reflected from a straight line it passes through the centre of the circle. Find the equation of this straight line if its perpendicular distance from P is 
. You can assume that the angle of incidence is equal to the angle of reflection.
Text Solution
Verified by Experts4
(4 
− 3) x − (4 + 3 
) y − (39 − 2 
) = 0
Let the equation of required straight line be y = mx + c.
⇒ 
= 
.....(i)
For Δ PCM 
= tan 2 α .
⇒ PM = 5cot 2 α .....(ii)
For Δ PQM 
= PM sin (90 – α ) ⇒ 
= 
cos α.
on solving, we get α = 30°. Equation of tangent at P(– 2, – 2) is 3x + 4y + 14 = 0.
tan 60° = 
⇒ 
= 
⇒ m = 
Now on substituting value of 'm' in equation (i), we get
c = 
or 
but c should be (–ve)
So equation of line y = 
x + 
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