Line `x-y=1` intersect the parabola `y^(2)=4x` at A and B. Normals at A and B intersect at C. If D is the point at which line CD is normal to the para

Question

Line `x-y=1` intersect the parabola `y^(2)=4x` at A and B. Normals at A and B intersect at C. If D is the point at which line CD is normal to the para

Line `x-y=1` intersect the parabola `y^(2)=4x` at A and B. Normals at A and B intersect at C. If D is the point at which line CD is normal to the parabola, then coordinate of point D is
A. `(4,-4)`
B. (4,4)
C. `(-4,-4)`
D. None of these

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
`(Sigmax_(i))/(10)=2" and "sqrt((Sigma(x_(i)-2)^(2))/(10))=3`
`(Sigma(x_(i)+1)^(2))/(10)=(1)/(10).Sigma(x_(1)-2+3)^(2)=(1)/(10).[Sigma(x_(i)-2)^(2)+6.Sigma(x_(i)-2)+3^(2).(10)]`
`=(1)/(10).[90+6.(20-20)+90]=18`

4 views Answered 2023-02-05 15:29