If the line y-m x-1 is tangent to the parabola y2-4 x- then find the value of m- -NCERT EXEMPLAR-

We have y2 = 4x Substituting the value of nbsp; y = mx + 1 in y2 = 4x, we get (mx + 1)2 = 4x rArr; m2x2 + 2mx + 1 = 4x rArr; m2x2 + (2m minus; 4)x + ...

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Standard XII

Mathematics

Tangent of a Curve y =f(x)

If the line y...

Question

If the line y = mx + 1 is tangent to the parabola y² = 4x, then find the value of m. [NCERT EXEMPLAR]

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Solution

We have y² = 4x
Substituting the value of y = mx + 1 in y² = 4x, we get
(mx + 1)² = 4x
⇒ m²x² + 2mx + 1 = 4x
⇒ m²x² + (2m − 4)x + 1 = 0 .....(1)
Since, a tangent touches the curve at a point, the roots of (1) must be equal.
∴ D = 0
⇒ (2m − 4)² − 4m² = 0
⇒ 4m²−16m + 16 − 4m² = 0
⇒ m = 1

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If the line y = mx + 1 is tangent to the parabola y2 = 4x, then find the value of m. [NCERT EXEMPLAR]

If the line y = mx + 1 is tangent to the parabola y² = 4x, then find the value of m. [NCERT EXEMPLAR]