The condition that the chord `xcosalpha+ysinalpha=p=0` of `x^2+y^2-a^2=0` may subtend a right angle at the center of the circle is `a^2=2p^2` (b) `p^2=2a^2` `a=2p` (d) `c^2=a^2(2m+1`

Options

A. `a^(2)=2p^(2)`
B. `p^(2)=2a^(2)`
C. `a=2p`
D. `p=2a`

Answer

1

Explanation

The distance of the given line from the center of the circle `|p|`.
Now, the line subtends right angle at the center. Hence,
Radius `= sqrt(2) |p|`
or `a= sqrt(2)|p|`
or `a^(2)=2p^(2)`