Question:
The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2 = 4x\) is:
The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2 = 4x\) is:
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The equation of the normal to a parabola can be used to find the number of normals through a given point.
- For a parabola, use the standard equation for the normal and solve for the number of solutions.
- For a parabola, use the standard equation for the normal and solve for the number of solutions.
Updated On: Mar 11, 2025
- \(0\)
- \(1\)
- \(2\)
- \(3\)
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The Correct Option is D
Solution and Explanation
The number of normals to a parabola \(y^2 = 4ax\) that can be drawn through a given point \((x_1, y_1)\) is given by solving the equation of the normal to the parabola. In this case, solving for the number of normals through the point \( (9,6) \) gives us 3 solutions. Thus, the correct answer is \(\boxed{3}\).
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