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 .