At what point on the parabola `y^2=4x` the normal makes equal angle with the axes? `(4,4)` (b) `(9,6)` (d) `(4,-4)` (d) `(1,+-2)`

Question

At what point on the parabola `y^2=4x` the normal makes equal angle with the axes? `(4,4)` (b) `(9,6)` (d) `(4,-4)` (d) `(1,+-2)`

At what point on the parabola `y^2=4x` the normal makes equal angle with the axes? `(4,4)` (b) `(9,6)` (d) `(4,-4)` (d) `(1,+-2)`
A. (4,4)
B. (9,6)
C. (4,-4)
D. `(1,pm2)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
(4) We have a=1.
Normal at `(m^(2),-2m)" is "y=mx-2-m^(3)`
Given that normal makes equal angle with the axes, its slope is `m=pm1`.
Therefore, point P is `(m^(2),-2m)-=(1,pm2)`.

4 views Answered 2023-02-05 15:29