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The point on the curve y=(x-1)(x-2) at w...

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)

Text Solution

Verified by Experts

The correct Answer is:
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.
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OBJECTIVE RD SHARMA-TANGENTS AND NORMALS-Chapter Test
  1. The point on the curve y=(x-1)(x-2) at which the tangent makes an angl...

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  2. The abscissa of the point on the curve ay^2 = x^3, the normal at whic...

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  3. If the curves (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(l^2)-(y^2)/(m^2)=1c...

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  4. The length of normal at any point to the curve, y=c cosh(x/c) is

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  5. If the sub-normal at any point on y^(1-n)x^n is of constant length, th...

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  6. The angle of intersection of the curves y=x^(2), 6y=7-x^(3) at (1, 1),...

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  7. The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2) -2t -5 at...

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  8. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

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  9. The tangent and normal at P(t), for all real positive t, to the parabo...

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  10. If y=4x-5 is a tangent to the curve y^(2)=px^(3) +q at (2, 3), then

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  11. The curve y-e^(xy)+x=0 has a vertical tangent at the point :

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  12. If the parametric of a curve given by x=e^(t)cos t, y=et sin t, then t...

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  13. The length of the normal at t on the curve x=a(t+sint), y=a(1-cos t), ...

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  14. For the parabola y^(2)=4ax, the ratio of the subtangent to the absciss...

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  15. The length of the subtangent to the curve sqrt(x) +sqrt(y)=3 at the po...

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  16. The normal to the curve x=a(cos theta + theta sin theta), y=a(sin thet...

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  17. Tangents are drawn from the origin to the curve y=cos X. Their points ...

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  18. If m denotes the slope of the normal to the curve y= -3 log(9+x^(2)) a...

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  19. If m be the slope of the tangent to the curve e^(2y) = 1+4x^(2), then

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  20. If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at...

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  21. If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the lin...

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