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A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and OB are drawn to the circle x^(2)+y^(2)=8. Using this information, answer the following questions : The locus of circumcenter of DeltaAQB id t=2 is |
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Answer» X-2y+2=0 (1) The EQUATION of the circumcenter of `DeltaAQB` is `x^(2)+y^(2)-4+lamda(xalpha+ybeta-8)=0` Because it passes through (0,0), i.e., the center of the circle, `lamda=-(1)/(2)` Let the circumcenter be (h,k). Then, `h=(alpha)/(4),k=(beta)/(4)` `oralpha=4h,beta=4k` Also, `betat=alpha+2t^(2)` `oralpha-2beta+8=0""(becauset=2)` Substituting `alpha=4handbeta=4k`, we GET h-2k+2=0 Therefore, the locus is x-2y+2=0. |
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