A) 'a' can attain only rational values |
B) 'a' is irrational |
C) cannot be concyclic for any 'a' |
D) none of the above . |
A) 'a' can attain only rational values |
Since B and C are the ends of diameter as \( \Large \angle BAC\ is\ 90 ^{\circ} \) Equation of circle is
\( \Large x \left(x-1\right)+y \left(y-1\right) = 0 \)
=> \( \Large x^{2}+y^{2}-x-y = 0 \)
Now point D satisfies it
=> \( \Large 4a^{2}+9a^{2}-5a = 0 => a \left(13a-5\right) = 0 \)
=> \( \Large a = 0,\ a = \frac{5}{13} \)