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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+4y−11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y2−6x−8y+20=0 are(C)The line equidistant from both the lines(R)(3,−3)4x+2y+2=0 and 6x+3y−21=0,passes through(D)If one of the sides of a square is 3x−4y−12=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?

List IList II (A)Centre(s) of the circle(s) having radius 5 and(P)(4,6)touching the line 3x+4y−11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y2−6x−8y+20=0 are(C)The line equidistant from both the lines(R)(3,−3)4x+2y+2=0 and 6x+3y−21=0,passes through(D)If one of the sides of a square is 3x−4y−12=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?

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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+y2−6x−8y+20=0

∴ Centre ≡(3,4), which does not coincide with the mid-point of PR (or) QT

(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+y2−6x−8y+20=0

∴ Centre ≡(3,4), which does not coincide with the mid-point of PR (or) QT

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