The line 3x + 2y + 1 = 0 meets the hyperbola 4x 2 - y 2 = 4a 2 in the points P and Q. The coordinates of the point of intersection of the tangents at P and Q are
Text Solution
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The required point is clearly the pole of the given line.
Let (x 1 , y 1 ) be the pole of 3x + 2y + 1 = 0 ... (1)
w.r.t. the hyperbola 4x 2 - y 2 = 4a 2 ... (2)
Polar of (x 1 , y 1 ) w.r.t. (2) is 4xx 1 - yy 1 = 4a 2 ... (3)
As (1) and (3) represent the same line i.e. polar of (x 1 , y 1 ),
∴ ∴ comparing coefficients, we get
.
Hence the required point i.e. the pole of (1) is (-3a 2 , 8a 2 ).
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