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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 = sqrt2`

B

`3x + y = 3sqrt2`

C

`x + y = 3sqrt2`

D

` x + 3y = 3sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
Given x = 3` cos theta , y = 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`
`implies x + y = 3sqrt2`
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