Question

lf $(\alpha ,3)$ and $($3, 5 $)$ are the extremities of the diameter of a circle with centre at $(2,\beta )$.
Then the values of $\alpha$ and $\beta$ are:

• A. $\alpha =1,\beta =4$
• B. $\alpha =4,\beta -2$
• C. $\alpha =4,\beta =1$
• D. $\alpha =5,\beta =-3$

Answer 1

The correct option is A $\alpha =1,\beta =4$

$(\alpha ,3)$ and $(3,5)$ are the extremities of the circle having centre $(2,\beta )$.

$\therefore \frac{\alpha +3}{2}=2$ and $\frac{3+5}{2}=\beta$

$\Rightarrow \alpha =1$ and $\beta =4$