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The angle between the tangents to the cu...

The angle between the tangents to the curve `y=x^2-5x+6` at the point (2, 0) and (3, 0) is (a)`pi/2` (b) `pi/3` (c) `pi` (d) `pi/4`

A

`pi//3`

B

`pi//2`

C

`pi//6`

D

`pi//4`

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of the curve is `y=x^(2)-5x+6`
`therefore (dy)/(dx) = 2x-5`
Let `m_(1) and m_(2)` be the slopes of the tangents at P(2, 0) and Q(3, 0) to the given curve. Then,
`m_(1)=((dy)/(dx))_(p)=2xx2-5= -1, m_(2)=((dy)/(dx))_(Q)=2xx3 -5=1`
Clearly, `m_(1)m_(2)= -1`. So, required angle is `(pi)/(2)`
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OBJECTIVE RD SHARMA ENGLISH-TANGENTS AND NORMALS-Chapter Test
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  2. The abscissa of the point on the curve ay^(2)=x^(3), the normal at whi...

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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=a^(1-n)x^(n) is of constant length...

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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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  9. about to only mathematics

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

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  12. The tangent to the curve given by x = e^(t) cos t y = e^(t) " sin 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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  16. Find the euation of normal to the curve x=a( cos theta + theta sin th...

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  17. Tangents ar drawn to y= cos x from origin then points of contact for t...

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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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