The line `x-y=1` intersects the parabola `y^2=4x` at `A` and `B` . Normals at `Aa n dB` intersect at `Cdot` If `D` is the point at which line `C D` is

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The line `x-y=1` intersects the parabola `y^2=4x` at `A` and `B` . Normals at `Aa n dB` intersect at `Cdot` If `D` is the point at which line `C D` is

The line `x-y=1` intersects the parabola `y^2=4x` at `A` and `B` . Normals at `Aa n dB` intersect at `Cdot` If `D` is the point at which line `C D` is normal to the parabola, then the coordinates of `D` are `(4,-4)` (b) `(4,4)` `(-4,-4)` (d) none of these
A. (4,-4)
B. (4,4)
C. (-4,-4)
D. none of these

Monjur Alahi

5 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 - B
(2) solving the line y=x-1 and the parabola `y^(2)=4x`, we have
`(x-1)^(2)=x`
`orx^(2)-6x+1=0`
`orx=3pmsqrt(8)`
`:.y=2pmsqrt(8)`
Suppose point D is `(X_(3),y_(3))`. Then,
`y_(1)+y_(2)+y_(3)=0`
`or2+sqrt(8)+2-sqrt(8)+y_(3)=0`
`ory_(3)=-4`
Then `x_(3)=4`.
Therefore, the point is (4,4).

5 views Answered 2023-02-05 15:29