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Question #40734

Difficulty: 8/10 | 🟢 Free

The Question

A line $L$ passing through the point $P(2, 3)$ intersects the curve $C: |x - 2| + |y - 3| = 4$ at two distinct points $A$ and $B$ . If the area of the triangle $OAB$ (where $O$ is the origin) is $10$ sq. units, then the sum of all possible values of the slope of the line $L$ is:

Options

A.
$-\frac{8}{9}$
B.
$\frac{10}{9}$
C.
$-\frac{10}{9}$
D.
$\frac{8}{9}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Bridge

Practice problems that bridge the gap between foundational theory and advanced practical application.

Concepts Behind This Question

Parametric Form Manipulation|Determinant as Geometric Area/Volume|Geometrical Interpretation of Modulus

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to integrate parametric coordinates with the determinant area formula.

The primary trap lies in the absolute value generated by the determinant, which, when combined with the modulus from the curve's equation, creates a bifurcated non-differentiable equation $2|3 - 2m| = 5(1 + |m|)$ .

Students often drop the modulus prematurely or fail to check the validity of the roots within the assumed case intervals (e.g., accepting $m = -11$ for the case $m \ge 3/2$ ), leading to incorrect slope sums.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Straight Lines - Class 11
Concept	Parametric Form Manipulation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free