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  4. 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

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Q. 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______

Coordinate Geometry

Solution:

image
$OAB$ 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.