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Find the locus of the point which is suc...

Find the locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` form a triangle of constant area with the coordinate axes.

Text Solution

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The chord of constant of tangents from P(h,k) is `(hx)/(a^(2))+(ky)/(b^(2))=1`
It meetts the axes at the points `A((a^(2))/(h),0)andB (0,(b^(2))/(k))`
Area of the triangle , OAB is
`(1)/(2)*(a^(2))/(h)*(b^(2))/(k)=c` (constant)
`rArr hk=(a^(2)b^(2))/(2c)` (constant)
`rArr xy=(a^(2)b^(2))/(2c)`
This is the rquired equation of locus.
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