InterviewSolution
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InterviewSolution
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If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of tangents is (A) `9x^2-8y^2+18x-9=0` (B) `9x^2-8y^2-18x+9=0` (C) `9x^2-8y^2-18x-9=0` (D) ` `9x^2-8y^2+18x+9=0`A. `9x^(2)-8y^(2)+18x-9=0`B. `9x^(2)-8y^(2)-18x=0`C. `9x^(2)-8y^(2)-9=0`D. `9x^(2)-8y^(2)+18x+9=0` |
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Answer» Correct Answer - B Let a pair of tangents be drawn from the point `(x_(1),y_(1))` to the hyperbola `x^(2)-y^(2)=9` Then the chord of contact will be `x x_(1)-yy_(1)=9" (1)"` But the given chord of contact is `x = 9" (2)"` As (1) and (2) represent the same line, these equations should be identical and, hence, `(x_(1))/(1)=-(y_(1))/(0)=(9)/(9)or x_(1)=1,y_(1)=0` Therefore, the equation of pair to tangents drawn from (1, 0) to `x^(2)-y^(2)=9` is `(x^(2)-y^(2)-9)(1^(2)-0^(2)-9)=(x*1-y*0-9)^(2)` `" "("Using SS"_(1)=T^(2))` `"or "(x^(2)-y^(2)-9)(-8)=(x-9)^(2)` `"or "-8x^(2)+8y^(2)+72=x^(2)-18x+81` `"or "9x^(2)-8y^(2)-18x+9=0` |
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