NIMCET 2018
The slopes of the two lines differ by
Answer (Detailed Solution Below)View answer โพHide โด
Answer: Option B โ
Detailed Solution
Put : , i.e. .
, so or .
Difference .
โ Check
, giving the lines and .โ Common trap
(D) is the sum of slopes worked out with ; since , h is (and the sum is ).Quick tip
: slopes
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Pair of Straight Lines โ Preparation
This question tests your understanding of Pair of Straight Lines, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A pair of straight lines can be represented by a single second-degree equation. This topic covers the homogeneous equation ax^2 + 2hxy + by^2 = 0, which represents two lines through the origin, and the general equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0. Exam questions test the condition for the general equation to represent a pair of lines, the angle between the lines (tan theta = 2 sqrt(h^2 - ab) / |a + b|), the conditions for the lines to be perpendicular (a + b = 0) or coincident (h^2 = ab), and the sum and product of the slopes (-2h/b and a/b). Knowing these results directly turns most questions into short calculations. Practise the pair of straight lines questions below, each with a step-by-step solution.