Question

These are numeric entry type questions.
A circle is passing through the origin $O(0,0)$ and intersects the $x$-axis and the $y$-axis at $A(a$, $0)$ and $B(0,b)$, respectively, where $a$ and $b$ are integers. The number of circles that can we drawn such that the diameter of the circle is 15 units is______

Answer 1

Answer: 8

$OAB$ is a right triangle $OA=9,OB=12$, and $AB=15$.
(1) $A(9,0),B(0,12)$
(2) $A(12,0),B(0,9)$
(3) $A(-9,0),B(0,12)$
(4) $A(-12,0),B(0,9)$
(5) $A(-9,0),B(0,-12)$
(6) $A(-12,0),B(0,-9)$
(7) $A(+9,0),B(0,-12)$
(8) $A(12,0),B(0,-9)$
Eight circles can be drawn.