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 .