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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 xaxis at A and yaxis 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
h01=k01=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+212+12∣ ∣=1
2d=2

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