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Choose the correct answer in the line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is

\[(A)\; 1 \quad (B)\; 2 \quad (C)\; 3 \quad (D)\;\frac{1}{2}\]

1 Answer

  • $\large\frac{d}{dx}$$(x^n)=nx^{n-1}$
  • Equation of tangent $y=mx+1$
Step 1:
The equation of the curve is $y^2=4x$
Differentiating with respect to $x$
Step 2:
Slope of the tangent $=\large\frac{2}{y}$$=m$-----(1)
$(x_1,y_1)$ lies on $y^2=4x$
Equation of tangent $(x_1,y_1)$
We are given the equation of tangent
Step 3:
Comparing (3) and (4)
From (1) & (2)
Step 4:
Put these value in equation (5)
$\Rightarrow y_1=2$
Part (A) is the correct answer.
answered Aug 13, 2013 by sreemathi.v

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