Question

The area of the triangle formed by the tangent at the point $(\alpha ,\beta )$ on the circle $x^2+y^2=8^2$ and the coordinate axes is

• A. $\frac{49}{2\alpha \beta }$
• B. $\frac{14}{\alpha \beta }$
• C. $\frac{16}{\alpha \beta }$
• D. $\frac{32}{\alpha \beta }$

Answer 1

Answer: (D)

$\frac{32}{\alpha \beta }$

Equation of the tangent is $\alpha x+\beta y=8^2$,
which meets the coordinate axes at $A(\frac{8^2}{\alpha },0)$ and $B(0,\frac{8^2}{\beta })$
and the area of $△AOB=\frac{8^4}{2\alpha \beta }=\frac{32}{\alpha \beta }$