IIT-JEE Exam

Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

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IIT-JEE Other Question

The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is
[Note: The trace of a matrix is the sum of its diagonal entries.] Equation of the circle with AB as its diameter is