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The equation of tangent to the curve giv...

The equation of tangent to the curve given by
` x = 3 cos theta , y = 3 sin theta , at theta = (pi)/(4)` is

A

` x + y = sqrt(2)`

B

`3x + y = 3sqrt(2)`

C

`x + y = 3 sqrt(2)`

D

`x + 3y = 3sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` x = 3 cos theta , y = 3 sin theta `
On squaring and adding we get ` x^(2) + y^(2) = 9 ` , which
represent a circle .
` therefore ` Equation of tangent at ` theta = (pi)/(4)` is
`x.(3 cos ""(pi)/(4)) + y . (3 sin "" (pi)/(4)) = 9 rArr x + y = 3 sqrt(2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
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  3. The equation of tangent to the curve given by x = 3 cos theta , y ...

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  4. Differentiate (logx)^x with respect to logx .

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  5. If x sec theta , y = tan theta , then the value of (d^(2) y)/(dx^(...

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  6. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

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  7. Find (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta and y = 2sin...

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  8. find the derivative of e^(x) + e^(y) = e^(x +y)

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  9. If xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) is equal to

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  10. The derivative of cos^(3)x w.r.t. sin^(3)x is

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  11. The derivative of log|x| is

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  12. The function f(x)=e^(-|x|) is

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  13. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

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  14. If y = log(cos x) sin x " then" (dy)/(dx) is equal to

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  15. If y^(2) = ax^(2) + bx + c , where a,b,c, are constants , then y^...

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  16. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

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  17. If y = 5^(x) x^(5) , " then" (dy)/(dx) is

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  18. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

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  19. (d)/(dx)[sec{cos^(-1) ((x)/(8))}] is equal to

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  20. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

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