NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

A line with gradient 2 intersects a line with gradient 6 at the point 40,30 . The distance between y -intercepts of these lines is

Options

A160
B180
C108
D120

Correct answer

A. 160

Step-by-step solution

Let C 1 and C 2 be the x -intercept of line with slope 2 and 6 respectively. y - 0 = 2 x - C 1 y = 2 x - 2 C 1 … … . i Similarly y = 6 x - 6 C 2 … … . i i Both i and i i satisfy x = 40 and y = 30 30 = 80 - 2 C 1 ⇒ C 1 = 25 And 30 = 240 − 6 C 2 ⇒ 6 C 2 = 210 ⇒ C 2 = 35 Hence, 6 C 2 - 2 C 1 = 160

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