1Anyone ??
An ellipse is described using an endless string which is passed over two pins.If the axes are 6 cm and 4 cm,the necessary length of the string and distance between them in cm are ???
Ans.6,2√5
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4 Answers
1Let the eqn. of the ellipse be x2 / a2 + y2 / b2 = 1
2 a = 6 cm { Given
2 b = 4 cm { Given
Hence eccentricity e = √1 - b 2 / a2 = √5 / 9 = √5 / 3
Clearly , the vetices of the elipse are ( -3 ,0 ) and ( 3 , 0) . Hence , the effective length of the string should be 6 cm so that it covers the max. distance of 6 চm between the 2 vertices .
And the dist. between the focis =dist. between the nails = 2 a e = 6 x √5 / 3 = 2 √5
