InterviewSolution
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InterviewSolution
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Match the following lists : |
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Answer» a. TANGENT to the parabola having slope m is `ty=X+t^(2)`. It passes through the point (2,3). Then, `3t=2+t^(2)`, i.e., t=1 or 2. The point of contact is (1,2) or (4,4) B. Let a point on the circle be `P(x_(1),y_(1))`. Then the chord of contact of the parabola w.r.t P is `yy_(1)=2(x+x_(1))`. Comparing with y=2(x-2), we have `y_(1)=1andx_(1)=-2`, which also satisfy the circle. c. Point Q on the parabola is at `(t^(2),2t)`. Now, the area of triangle OPQ is `|(1)/(2)|:(0,0),(4,-4),(t^(2),2t),(0,0):||=6or8t+4t^(2)=pm12` For`t^(2)+2t-3=0,(t-1)(t+3)=0`. Then t=1 or t=-3. Then point Q is (1,2) or (9,-6). d. Point (1,2) and (-2,1) satisfy both the curves. |
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