If the family of straight lines a x + b y + c = 0 , where 2 a + 3 b = 4 c is concurrent at the point P l , m , then the foot of the perpendicular drawn from P to the line x + y + 1 = 0 is

Question

If the family of straight lines a x + b y + c = 0 , where 2 a + 3 b = 4 c is concurrent at the point P l , m , then the foot of the perpendicular drawn from P to the line x + y + 1 = 0 is, - 3 8 , - 5 8, - 2 5 , - 3 5, 3 , - 4, - 5 , 4

MARKS App · Accepted Answer

Line a x + b y + c = 0 is compared with - a 2 - 3 b 4 + c = 0 x = - 1 2 , y = - 3 4 ⇒ P - 1 2 , - 3 4 Now, Foot of ⊥ ⇒ x + 1 2 1 = y + 3 4 1 = - - 1 2 - 3 4 + 1 2 ⇒ x + 1 2 = y + 3 4 = - 1 8 ⇒ x = - 3 8 , y = - 5 8

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