    Question

# Match List I with the List II and select the correct answer using the code given below the lists : Let the line L:ax+by+c=0 intersect x−axis at A and y−axis at B. Let O be the origin. List IList II(I)If a,b,c are in G.P. with common ratio as 2, then area of ΔAOB is(P)6(II)If a=1,b=1,c=2 and circumradius of ΔAOB is √p,p>0, then the value of 3p is(Q)4(III)If a=b=c=1 and reflection of O along the line L is (α,β), then |α+β| is (R)2(IV)If a=b=1,c=√2 and d is the shortest distance of line L from O, then 2d is (S)3(T)1 Which of the following is CORRECT combination?

A
(I)(R); (II)(S); (III)(Q); (IV)(P)
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B
(I)(Q); (II)(T); (III)(P) (IV)(R)
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C
(I)(Q); (II)(T); (III)(S); (IV)(R)
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D
(I)(Q); (II)(P); (III)(R); (IV)(R)
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Solution

## The correct option is D (I)→(Q); (II)→(P); (III)→(R); (IV)→(R)ax+by+c=0 A : (−ca,0) B : (0,−cb) O : (0,0) Area of ΔAOB =12×∣∣∣ca×cb∣∣∣=c22ab (I) a,b,c are in G.P. with common ratio as 2 Area of ΔAOB=c22ab=4 (II) Since a=1,b=1,c=2 and AB is the hypotenuse of the triangle AOB ∴ Circumradius is half of AB i.e., √2 (III) Since a=b=c=1, so the reflection (h,k) of O along the line x+y+1=0 is h−01=k−01=−2(0+0+1)2 h=−1 and k=−1 (IV) For the line x+y+√2=0, shortest distance from the origin is d=∣∣ ∣∣0+0+√2√12+12∣∣ ∣∣=1 ⇒2d=2  Suggest Corrections  0      Related Videos   Straight Line
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