35) answer is b...if dat is not given as the answer it is wrong!!
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)
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2 Answers
333) i am getting the answer as c
Any point on the given parabola is (t2+1, 2t)
condition for two points to lie on a focal chord is t1t2=--1
thus the other point is given by [1/t2+1,--2/t]
thus the slope of the line joining them(by solving) is
2t/(t2--1)=m (given)
we thus get a quadratic in "t" which is
mt2-2t--m=o
as t must be real,
D>0
4+4M2>0 WHICH IS TRUE FOR ALL m thus m belongs to real!! I hope this is correct :)
