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IIT JEE SOLVED PAPERS ON CO-ORDINATE GEOMETRY(2D)

Here is some solved questions from IIT-JEE papers




Q. [IIT-JEE 2001]The equation of the directrix of the parabola          y2 + 4y +4x + 2 = 0 is
(a) x = -1      (b) x = 1      (c) x = -3/2      (d) x = 3/2
Solution :(d) Equation of the given parabola is (y+2)2 = - 4(x – ½)
Let   x – ½ = X,   y + 2 = Y . Then the above equation reduces to        Y2 = -4X . Equation of directrix is x – ½ = 1.
Q. [IIT-JEE 1998] The number of values of c such that the straight line y = 4x + c touched the curve   x2/4 + y2 = 1 is
(a) 0     (b) 1     (c) 2     (d) infinite
Solution :(c) The line y = mx + c touches the ellipse                      x2/a2 + y2/b2 =1 if c = ± √(a2m2+b2).
Thus, number of values of c is 2.
Q. [IIT-JEE 2002] The equation of the common tangent to the curves  y2 = 8x and  xy = -1 is
(a) 3y=9x+2    (b) y=2x+1     (c) 2y=x+8     (d) y=x+2
Solution :(d) Let equation of tangent to parabola  y2 = 8x be               y = mx + 2/m --------------(1)
Let (1) meet the hyperbola  xy = -1 --------(2) at the point given by                             x( mx + 2/m )=-1     m2x2 + 2x + m = 0 -------------(3)
Since the equation (1) is tangent to (2), equation (3) must have equal roots, for which  D = 0  4 – 4m2 = 0  m = 1.
From (1), equation of the common tangent is  y = x + 2 .