The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is

(A) 1 (B) 2 (C) 3 (D)

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Solution

The equation of the tangent to the given curve is y = mx + 1.

Now, substituting y = mx + 1 in y² = 4x, we get:

Since a tangent touches the curve at one point, the roots of equation (i) must be equal.

Therefore, we have:

Hence, the required value of m is 1.

The correct answer is A.

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Similar questions

Q. The line y = mx + 1 is a tangent to the curve y 2 = 4 x if the value of m is (A) 1 (B) 2 (C) 3 (D)

Choose the correct answer in the following questions :
The line y=mx + 1 is a tangent to the curve $y^{2} = 4 x,$ if the value of m is
(a) $1$ (b) $2$ (c) $3$ (d) $\frac{1}{2}$

Q. The line

y = m x + 1

is a tangent to the curve

y^{2} = 4 x

, if the value of

m

Q. The line y = mx + 1 is a tangent to the curve y² = 4x, if the value of m is

(a) 1
(b) 2
(c) 3
(d)

\frac{1}{2}

Q. Mark the correct alternative of the following.
The line

y = m x + 1

is a tangent to the curve

y^{2} = 4 x

, if the value of m is?

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The line y = mx + 1 is a tangent to the curve y2 = 4x if the value of m is (A) 1 (B) 2 (C) 3 (D)

The equation of the tangent to the given curve is y = mx + 1. Now, substituting y = mx + 1 in y2 = 4x, we get: Since a tangent touches the curve at one point, the roots of equation (i) must be equal. Therefore, we have: Hence, the required value of m is 1. The correct answer is A.

The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is

(A) 1 (B) 2 (C) 3 (D)

The equation of the tangent to the given curve is y = mx + 1.

Now, substituting y = mx + 1 in y² = 4x, we get:

Since a tangent touches the curve at one point, the roots of equation (i) must be equal.

Therefore, we have:

Hence, the required value of m is 1.

The correct answer is A.