Question:
The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are
The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are
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The shortest distance from a curve to a line occurs where the tangent is parallel to the line.
Updated On: Apr 16, 2026
- \((-2, -8)\)
- \((1, 10)\)
- \((2, 20)\)
- \((-1, -4)\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The nearest point on the parabola to the line is where the tangent is parallel to the line.
Step 2: Detailed Explanation:
Slope of line = 3. For parabola, \(dy/dx = 2x + 7\). Set equal to 3: \(2x + 7 = 3 \Rightarrow 2x = -4 \Rightarrow x = -2\). Then \(y = (-2)^2 + 7(-2) + 2 = 4 - 14 + 2 = -8\). So point is \((-2, -8)\).
Step 3: Final Answer:
\((-2, -8)\), which corresponds to option (A).
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