Question
Hard
Solving time: 5 mins
Let be three points on parabola and normal at and meet at , then the locus of the midpoint of the chord is a parabola whose vertex is at
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Text solutionVerified
Let and be three points on such that normal at and intersect at .
Then,
Let be the mid-point of . Then, and
Now,
So, the locus of is
or,
Clearly, it represents a parabola having vertex at
Then,
Let be the mid-point of . Then, and
Now,
So, the locus of is
or,
Clearly, it represents a parabola having vertex at
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Question Text | Let be three points on parabola and normal at and meet at , then the locus of the midpoint of the chord is a parabola whose vertex is at
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Topic | Conic Sections |
Subject | Mathematics |
Class | Class 11 |
Answer Type | Text solution:1 |
Upvotes | 21 |