Match the following :
Column-I | Column-II |
(i) The reflection of the point (t – 1, 2t + 2) in a line is (2t + 1, t) then the line has slope equal to | [A] 5 |
(ii) If θ be the angle between two tangents which are drawn to the circle x2 + y2 – 6 x – 6y + 27 = 0 from the origin, then 2 tanθ equals to | [B] 6 |
(iii) The shortest distance between parabolas y2 = 4x and y2 = 2x – 6 is d then d2 = | [C] |
(iv) Distance between foci of the curve represented by the equation x = 1 + 4cosθ, y = 2 + 3sinθ is | [D] 1 |
Text Solution
Verified by Experts(i) [D]; (ii) [B]; (iii) [A]; (iv) [C]; (I) (0, 0); (III) (4, 4)
Ans.
(i) [D]
(ii) [B]
(iii) [A]
(iv) [C]
Sol. (i) Slope of line = 
= 
= 1
(ii)
Let y = mx is the tangent drawn from origin. Then
3 = 
1 + m 2 = 
⇒ 1 + m 2 = 1 + 3m 2 – 
m
⇒ 2m 2 – 
m = 0 ⇒ m = 0, 
So angle between tangents tan θ = 
= 
so 
tan θ = 6.
(iii)
y 2 = 4x .....(1)
y 2 = 2(x – 3) .....(2)
equation of normal at (1) is
y = mx – 2m – m 3 .....(3) at (m 2 , –2m)
equation of normal of same slope
y = m(x – 3) – m – 
....(4) at 
if (3) & (4) represent same line then
–2m – m 3 = –3m – m – 
⇒ 2m – 
= 0
m = 0, ±2
so foot of normals are (I) (0, 0) & (3, 0)
(ΙΙ) (4, –4) & (5, –2)
(III) (4, 4) & (5, 2)
So possible values of d = 3, 
So d min = 
⇒ d 2 = 5
(iv) equation of curve 
= 1
Distance between the focii is
= 2ac = 
= 
= 
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