Question

The line $y = mx + 2$ is a tangent to the parabola $y^{2} = 8x$ if}

• A. $m = 1$
• B. $m = 2$
• C. $m = 3$
• D. $m = 4$

Hint:

Remember $c = a/m$ for $y^2 = 4ax$. It’s a shortcut that avoids using the discriminant method ($\Delta = 0$).

Answer 1

The Correct Option is A

Step 1: Concept
For a line $y = mx + c$ to be a tangent to the parabola $y^{2} = 4ax$, the condition is $c = a/m$.

Step 2: Meaning
From $y^{2} = 8x$, we find $4a = 8$, so $a = 2$. From the line $y = mx + 2$, we have $c = 2$.

Step 3: Analysis
Apply the condition $c = a/m$: $2 = 2/m$.

Step 4: Conclusion
Solving for $m$ gives $m = 1$.
Final Answer: (A)