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Question

If A=(at2,2at),B=(at2,2at),S(a,0) then 1SA+1SB=

A
a
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B
1a
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C
2a
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D
2aa
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Solution

The correct option is B 1a
Distance formula: The distance between points (x1,y1) and (x2,y2) is given by (x2x1)2+(y2y1)2
A=(at2,2at),B=(at2,2at),S(a,0)SA=(aat2)2+(02at)2=a2+a2t42a2t2+4a2t2=a2+a2t4+2a2t2=(a+at2)2=a+at2SB=(aat2)2+(0+2at)2=a2+a2t4+4a2t22a2t2=a2+a2t4+2a2t2=(a+at2)2=a+at2Now,1SA+1SB=1a+at2+1a+at2=1a+at2+t2a+at2=(1+t2)a(1+t2)=1a

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