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P is a variable points on the hyperbola `x^2/a^2-y^2/b^2=1` whose vertex is `A(a,0)` The locus of the middle points AP isA. `((2x-a)^(2))/a^(2)-(2y^(2))/b^(2)=1`B. `((2x-a)^(2))/a^(2)-(4y^(2))/b^(2)=1`C. `((2x-a)^(2))/a^(2)-(8y^(2))/b^(2)=1`D. None of these |
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Answer» Correct Answer - 2 Let the point P be `(a sectheta, b tantheta)` and A(a, 0), let the point of AP be (h, k) `therefore h=(a+asectheta)/2 and k=(btantheta)/2` `rArr(2h-a)/a=sectheta…(i)` and `(2k)/b=tantheta…(ii)` Squaring and Subtracting (ii) from (i) we get `rArr((2h-a)^(2))/a^(2)-(4y^(2))/b^(2)=1` |
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