Straight Lines · Question 23

JEE Main 2025 (Online) 2nd April Evening ShiftMCQEasy📈 Topic in 10% papers+4−1

Let the area of the triangle formed by a straight line L : x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of 45 with the positive x-axis, then the value of b2 + c2 is :

Answer

(4) 97

Solution

Normal form of the line: x 45 + y 45 = p

x + y = 2p

Comparing with x + by + c = 0: b = 1, c = - 2p

L: x + y + c = 0 meets the axes at (-c, 0) and (0, -c)

Area = 12|c| |c| = 48 c2 = 96

b2 + c2 = 1 + 96 = 97

Answer: (4)

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JEE Main 2025 (Online) 28th January Evening Shift

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