Match the column:
Column-I | Column-II |
(i) If (α, β) is a point on circle whose centre is on x axis which touches line y = –x at (2, –2) then greatest value of α is | [A] 22 |
(ii) The sum of squares of length of chords intercepted by line x + y = n, n ∈ N on circle x2 + y2 = 4 | [B] 0 |
(iii) If point (a, a) lies between lines |x + y | = 6 then [ | a | ] is([ . ] denote greatest integer) | [C] 1 |
(iv) No. of points from where perpendicular tangents can be drawn on | [D] 4+ 2 |
[E]2 |
Text Solution
Verified by Experts(i) [D]; (ii) [A]; (iii) [B]; (iv) [B]
Ans.
(i) [D]
(ii) [A]
(iii) [B],[C],[E]
(iv) [B]
Sol.
(i)
slope of line = –1
∴ ∠ COM = 45º
∴ OM = 
So OC = 4
∴ So α will be maximum at point B
∴ α = 4 + 
(ii)
Line will cut circle if
OM < 2 ....(i)
Now OM = 
....(ii)
As n ∈ N so n = 1 and 2 can satisfy (i) and (ii)
Length AB = 2 AM = 
AB 2 = 
= 16 – 2n 2 Required sum = (16 – 2) + (16 – 2.2)
2 = 22
(iii)
The point (a, a) lies on y = x
Solving it with x + y = 6
We get coordinates of A(3, 3)
Similarly coordinates of B(–3, –3)
∴ –3 < a < 3 {point lies between lines}
⇒ 0 ≤ | a | < 3
⇒ [ | a | ] = 0, 1, 2
(iv) Equation of director circle is
x 2 + y 2 = a 2 – b 2 (a > b)
here x 2 + y 2 = –1
not possible
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