Question

Assertion :The point of intersection of the tangent at three distinct points $A,B,C$ on the parabola $y^2=4x$ can be collinear. Reason: If a line $L$ does not intersect the parabola $y^2=4x$, then from every point of the line two tangents can be drawn to the parabola.

• 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 incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

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

Area of the triangle by the intersection points of tangents at $A\left(t_1\right),B\left(t_2\right),C\left(t_3\right)$ is given by $\frac{1}{2}|t_2-t_1||t_2-t_3||t_3-t_1|\ne 0$
$\therefore$ Points A, B, C cannot be collinear $\Rightarrow$ Assertion (A) is false but Reason (R) is correct