Application of Derivatives 4 Question 44
46. Let and be respectively, the parabolas and . Let be any point on and be any point on . If and is the reflections of and , respectively, with respect to the line . Prove that lies on lies on and . Hence, determine points and on the parabolas and respectively such that for all pairs of points with on and on .
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Answer:
Correct Answer: 46.
Solution:
- Let coordinates of
be
Reflection of
which clearly lies on
Similarly, let coordinates of
Its reflection in
We have,
Also
Thus,
Also,
Let us take
[say] we have,
Now,
Also,
and
Thus,
Corresponding to