Question

The point on the curve `y=(x-1)(x-2)` at which the tangent makes an angle of `135^(@)` with the positive direction of x-axis has coordinates
A. (1, 0)
B. (0, 1)
C. (-1, 0)
D. (0, -1)

Answer 1

Correct Answer - A
Let `(x_(1),y_(1))` be the required point . Then,
`((dy)/(dx))_((x_(1)","y_(1)))=tan 135^(@)`
`rArr 2x_(1)-3= -1 " " [ because y=(x-1)(x-2)rArr (dy)/(dx) =2x-3] `
`rArr x=1`
Since `(x_(1),y_(1))` lies on `y=(x-1)(x-2).`
`therefore y=(x_(1), -1)(x_(1)-1)=(1-1)(1-2)=0`
Hence, (1, 0) is the required point.