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Question

If A(a2,2a)B(1a2,2a) and S(1,0) then prove that 1SA+1SB=1

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Solution

SA=(1a2)2+(2a)2
=1+a42a2+4a2
=1+a4+2a2
=(1+a2)2
=(1+a2) ..........1

SB=(11a2)2+(2a)2
=1+1a42a2+4a2
=1+1a4+2a2
=(1+1a2)2
=1+1a2
=a2+1a2 ......2

Then,1SA+1SB=11+a2+a21+a2
=1+a21+a2=1

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