26. S is one focus of an ellipse an...

26. S is one focus of an ellipse and P is any point on the ellipse. If the maximum and minimum values of SP are m and n respectively, then the length of semi major axis is 1) AM ofm,n 2) G.M. ofm,n 3) HM ofm,n 4) AGP ofm,n

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( (x, y) quad x=a cos theta ) ( y=6 sin theta ) ( Rightarrow m= ) max when Pis at A or B for sqor Sy respt.. An on ( n= ) min when Pis at ( A ) or ( B ) for S, or S ( _{2} ) respt ( 2 a e=m-n ) ( a e=frac{m-n}{2} Rightarrow 0 S_{1}=frac{m-n}{2} quad s_{1} A=n ) given (ength of seme major axis ( Rightarrow quad Rightarrow 0 S_{1}+S_{1} A=frac{m-n}{2}+frac{2 n}{2}=frac{m+n}{2} )
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