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The locus of mid points of the portions of the tangents to the ellipse x 2 /a 2 +y 2 /b 2 =1 included between the axes is the curve?

The locus of mid points of the portions of the tangents to the ellipse x2/a2 +y2/b2=1 included between the axes is the curve?
 

Grade:12

1 Answers

Faiz
107 Points
7 years ago
Tangent at any point to the ellipse (acos ß, bsin ß) is xcosß / a + ysinß / b = 1....It mmets yhe axes in points (a secß,0) and (0,b coseß).....Lets the mid point be (h,k) then h= a secß / 2 and k = b cosecß / 2......Rearranging we get, cosß= a/2h and sinß= b/2k....Eliminating ß by squaring and adding.....which gives the locus as::::::::ans... a²/x² + b²/y² = 4.......

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