1)The triangle formed by the tangent to the curve f(x) = x2 + bx - b at the point (1,1) and the co-ordinate axes lie in the first quadrant. If it's area is 2 then the value of b is:
a)-1 b)3 c)-3 d)1
ans c
2)If the normals from any point to the parabola x2 = 4y cuts the line y = 2 in points whose abscissae are in AP , then the slopes of the tangents at the three co-normal points are in:
a) AP b)GP c) HP d) None of these
ans b
3)A line L passing through the focus of the parabola y2 = 4(x-1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then:
a) m E (-1,1) b) m E (-∞,-1) U (1 , ∞) c) m E R d) None of these
ans d
4)The latus rectum of the parabola x = at2 + bt + c and y = a't2 + b't + c' is
a)(aa' - bb')2(a2 + a'2)3/2 b)(ab' - a'b)2(a2 + a'2)3/2 c) (bb' - aa')2(b2 + b'2)3/2 d)(a'b - ab')2(b2 + b'2)3/2
ans b
5)answer not matching
If the tangents to to the parabola y2 = 4ax at the points (x1 , y1) and (x2 , y2) meet at (x3 , y3) then:
a)y3 = √y1y2 b) 2y3 = y1 + y2 c)2y3 = 1y1 + 1y2 d) None of these.
book answer a my answer b
1 to 4 are doubts (please give the solutions) and 5 I am not getting the answer as given by the book..(someone please confirm which is the correct answer)