EllipseMedium
Question
If a > 2b > 0 then positive value of m for which y = mx - b 
is a common tangent tox2 + y2 = b2 and (x - a)2 + y2 = b2 is
is a common tangent tox2 + y2 = b2 and (x - a)2 + y2 = b2 is Options
A.
B.
C.
D.
Solution
Given, y = mx - b touches both the circles, so distance from centre = radius of both the circles.
and
⇒
⇒ m2a22 - 2abm
b2 (1+ m2) = b2 (1 + m2)
⇒ ma - 2b
= 0
⇒ m2a2 = 4b2 (1 + m2)
⇒
touches both the circles, so distance from centre = radius of both the circles.and
⇒
⇒ m2a22 - 2abm
b2 (1+ m2) = b2 (1 + m2)⇒ ma - 2b
= 0⇒ m2a2 = 4b2 (1 + m2)
⇒
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