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Question

List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II.

List IList II (A)Centre(s) of the circle(s) having radius 5 and(P)(4,6)touching the line 3x+4y11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y26x8y+20=0 are(C)The line equidistant from both the lines(R)(3,3)4x+2y+2=0 and 6x+3y21=0,passes through(D)If one of the sides of a square is 3x4y12=0(S)(2,7)and its centre is (0,0), then its diagonalpasses through(T)(2,2)

Which of the following is the only CORRECT combination?

A
(A)(P),(S)
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B
(A)(P),(T)
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C
(B)(P),(R)
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D
(B)(Q),(T)
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Solution

The correct option is B (A)(P),(T)
(A)

Slope of tangent =34
Slope of C1C2=43=tanθ
cosθ=35, sinθ=45
By parametric form,
C1,C2(1±5cosθ,2±5sinθ)
=(1±3,2±4)=(4,6),(2,2)

(B)
Given circle is x2+y26x8y+20=0
Centre (3,4), which does not coincide with the mid-point of PR (or) QT

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