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If the line y cos alpha = x sin alpha +...

If the line ` y cos alpha = x sin alpha +a cos alpha ` be a tangent to the circle `x^(2)+y^(2)=a^(2)`, then

A

`sin^2alpha=1`

B

`cos^2alpha=1`

C

`sin^2alpha=a^2`

D

`cos^2alpha=a^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `y=xtan alpha+a`
Condition for tangency is `a^2=a^2(1+tan^2alpha)[because c^2=a^2(1+m^2)]`
`rArr sec^2alpha=1rArr cos^2=1`
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