For which value of m is the line y = mx + 1 a tangent to the curve y2

1.	For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x ?(a) 1/2(b) 1(c) 2(d) 3
Answer» Option : (b) y = mx + 1 … . . (1) and y² = 4x … … (2) Substituting (1) in (2) : (mx + 1)² = 4x ⇒ m²x² + (2m − 4)x + 1 = 0 … … . . (3) As line is tangent to the curve ⇒ line touches the curve at only one point ⇒ (2m − 4)² − 4m² = 0 ⇒ m = 1

For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x ?(a) 1/2(b) 1(c) 2(d) 3

Answer»

Option : (b)

y = mx + 1 … . . (1) and

y² = 4x … … (2)

Substituting (1) in (2) :

(mx + 1)² = 4x

⇒ m²x² + (2m − 4)x + 1 = 0 … … . . (3)

As line is tangent to the curve

⇒ line touches the curve at only one point

⇒ (2m − 4)² − 4m² = 0

⇒ m = 1

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For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x ?(a) 1/2(b) 1(c) 2(d) 3

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