The point on the curve y = x - 1 where the tangent is perpendicular to the line 2 x + y - 5 = 0 is

Question

The point on the curve y = x - 1 where the tangent is perpendicular to the line 2 x + y - 5 = 0 is, ( 2 , − 1 ), ( 10 , 3 ), ( 2 , 1 ), ( 5 , − 2 )

MARKS App · Accepted Answer

For given curve, d y d x = 1 2 x - 1 = m 1 (say) Now Slope of line 2 x + y - 5 = 0 is m 2 = - 2 Since lines are perpendicular ⇒ m 1 m 2 = - 1 ⇒ 1 2 x - 1 - 2 = - 1 ⇒ 2 2 x - 1 = 1 ⇒ x - 1 = 1 ⇒ Squaring both sides, x - 1 = 1 ⇒ x = 2 ⇒ y = x - 1 = 2 - 1 = 1 = 1 So the required point is 2 , 1

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