Question

Assertion :Number of circle passing through $(1,4)$, $(2,3)$, $(-1,6)$ is only one. Reason: Through three non collinear points in a plane only one circle can be drawn.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

It is true thal through three non collinear points a unique circle passes through.
Now by points $(1,4),(2,3),(-1,6)$ we have $\Delta =\frac{1}{2}\left|\begin{array}{ccc}1& 4& 1\\ 2& 3& 1\\ -1& 6& 1\end{array}\right|=0$
$\Rightarrow$ Points are collinear, so no circle can be drawn
$\therefore$ Assertion (A) is false but Reason (R)is true.