C1 and C2 are two circles whose equations are given as x2 + y2 = 25 and x2 + y2 + 10x + 6y + 1 = 0. Now C3 is a variable circle which cuts C1 and C2 orthogonally. Tangents are drawn from the centre of C3 to C1, if the locus of the mid point of the chord of contact of tangents is ax + 3y +
(where a, b
Z+, and a and b are relative prime), then
is
C1 and C2 are two circles whose equations are given as x2 + y2 = 25 and x2 + y2 + 10x + 6y + 1 = 0. Now C3 is a variable circle which cuts C1 and C2 orthogonally. Tangents are drawn from the centre of C3 to C1, if the locus of the mid point of the chord of contact of tangents is ax + 3y + (where a, b Z+, and a and b are relative prime), then is
Option 1 -
1
Option 2 -
2
Option 3 -
4
Option 4 -
5
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1 Answer
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Correct Option - 4
Detailed Solution:Centre of C3 will lie on the radical axis of C1 and C2 which is 10x + 6y + 26 = 0.
Let center of C3 is (h, k).
Equation of chord of contact through (h, k) to the C1 may be given as hx + ky = 25 … (I)
Let the mid point of the chord is (x1, y1) the equation of the chord with the help of mid point may be given as
Since (I) and (II) represents same straight line 10x + 6y + 26 = 0
The locus of (x1, y1) is
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