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Find locus of the point moving such that sum of their distances from(3,0) and(-3,0) is less than 9 units. Plz explain me the normal method as well as the other one in which we take PA+PB=2a and AB=2ae
Find locus of the point moving such that sum of their distances from(3,0) and(-3,0) is less than 9 units.
Plz explain me the normal method as well as the other one in which we take PA+PB=2a and AB=2ae
Dear karhik, the locus will be all the points INSIDE the ellipse as the definition of ellipse says that it is the locus all the points whose sum of distances from the fixed points (focii) is constant and that is equal to 2 a where coordinates of focii are (ae,0) and (-ae,0) so if the distance is less than 9 2a = 9 a=9/2 ae = 3 e = 2/3 b2 = a2 (1 - e2 ) b2 = 45/4 a2 = 81/4 ellipse is x2 /(81/4) + y2 /(45/4) = 1 alternate method let the point be (h,k) use distance formula {(h-3)2 + (k-0)2}1/2 + {(h+3)2 + (k-0)2}1/2 = 9 (h-3)2 + (k-0)2}1/2 = 9 - {(h+3)2 + (k-0)2}1/2 now square it twice you will get the locus of the points and after getting the final equation we get the equation We are all IITians and here to help you in your IIT JEE preparation. Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar.. jitender
Dear karhik,
the locus will be all the points INSIDE the ellipse as the definition of ellipse says that it is the locus all the points whose sum of distances from the fixed points (focii) is constant and that is equal to 2 a where coordinates of focii are (ae,0) and (-ae,0) so if the distance is less than 9
2a = 9 a=9/2
ae = 3 e = 2/3
b2 = a2 (1 - e2 )
b2 = 45/4 a2 = 81/4
ellipse is x2 /(81/4) + y2 /(45/4) = 1
alternate method let the point be (h,k) use distance formula {(h-3)2 + (k-0)2}1/2 + {(h+3)2 + (k-0)2}1/2 = 9
(h-3)2 + (k-0)2}1/2 = 9 - {(h+3)2 + (k-0)2}1/2
now square it twice you will get the locus of the points and after getting the final equation we get the equation
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