CircleHard
Question
Pair of tangents are drawn from every point on the line 3x + 4y = 12 on the circle x2 + y2 = 4. Their variable chord of contact always passes through a fixed point whose co-ordinates are -
Options
A.
B.
C.(1, 1)
D.
Solution
Let P(x1, y1) be a point on the line 3x + 4y = 12.
Equation of variable chord of contact of P(x1, y1) wrt circle x2 + y2 = 4
xx1 + yy1 - 4 = 0 ......(1)
Also 3x1 + 4y1 - 12 = 0
x1 +
y1 - 4 = 0 .....(2)Comparing (1) & (2)
x = 1, y =
∴ variable chord of contact always passes through (1,
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