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The normal to the curve x=a(1+cos theta...

The normal to the curve `x=a(1+cos theta), y=a sin theta " at " 'theta ' ` always passes through the fixed point

A

(a, a)

B

(a, 0)

C

(0, a)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`x=a(1+cos theta), y=a sin theta.`
`therefore (dy)/(dx)=((dy)/(d theta))/((dx)/(d theta))=(a cos theta )/(-a sin theta)=-cot theta`
The equation of the normal at `(a(1+cos theta), a sin theta) ` is
`y-a sin theta =tan theta {x-a(1+cos theta)}`
`rArr x sin theta -y cos theta=a sin theta `
Clearly, it passes through (a, 0).
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OBJECTIVE RD SHARMA ENGLISH-TANGENTS AND NORMALS-Chapter Test
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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. What is the angle between these two curves x^3-3xy^2+2=0 and 3x^2y-y^3...

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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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  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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  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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