Question

Assertion :If the perpendicular bisector of the line segment Joining $P(1,4)$ and $Q(K.3)$ has $y$-intercept $-4,$ then $k^2-16=0$ Reason: Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the given points.

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reason is True, using in assertion

${(x-1)}^2+{(y-4)}^2={(x-K)}^2+{(y-3)}^2$

$\Rightarrow 2(K+1)x-2y=K^2-8$

$y-$intercept$=-\frac{K^2-8}{2}=-4\Rightarrow K^2-16=0$
showing that assertion is True