IIT-JEE Exam

Consider the two curves C1 : y^2 = 4x, C2 : x^2 + y^2 – 6x + 1 = 0. Then,
(A) C1 and C2 touch each other only at one point
(B) C1 and C2 touch each other exactly at two points
(C) C1 and C2 intersect (but do not touch) at exactly two points
(D) C1 and C2 neither intersect nor touch each other

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IIT-JEE Other Question

Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 – 5xy + 6y2) = 0 represents
(A) four straight lines, when c = 0 and a, b are of the same sign
(B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
(C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
(D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a. A tells B " if you give me Rs 400, then i shall have 25% more than what you have". B tells A, "if you give me Rs 200, then i shall have three- and - half times as much as you have."how much does B have.