Question
If $$\left( {a,\,b} \right)$$ is a point on the chord $$AB$$ of the circle, where the ends of the chord are $$A = \left( {2,\, - 3} \right)$$ and $$B = \left( {3,\,2} \right),$$ then :
A.
$$a\, \in \,\left[ { - 3,\,2} \right],\,b\, \in \,\left[ {2,\,3} \right]$$
B.
$$a\, \in \,\left[ {2,\,3} \right],\,b\, \in \,\left[ { - 3,\,2} \right]$$
C.
$$a\, \in \,\left[ { - 2,\,2} \right],\,b\, \in \,\left[ { - 3,\,3} \right]$$
D.
none of these
Answer :
$$a\, \in \,\left[ {2,\,3} \right],\,b\, \in \,\left[ { - 3,\,2} \right]$$
Solution :
$$\left( {a,\,b} \right)$$ should be an internal or end point of the line segment joining $$A,\,B.$$
So, the $$x$$-coordinate $$a$$ will vary from $$2$$ to $$3$$, i.e., from the $$x$$-coordinate of $$A$$ to the $$x$$-coordinate of $$B.$$ Similarly, for $$y$$-coordinate.