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If two of the three feet of normals draw...

If two of the three feet of normals drawn from a point to the parabola `y^2=4x` are (1, 2) and `(1,-2),` then find the third foot.

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To find the third foot of the normals drawn from a point to the parabola \( y^2 = 4x \), given that two of the feet are \( (1, 2) \) and \( (1, -2) \), we can follow these steps: ### Step 1: Understand the properties of the parabola The equation of the parabola is given by \( y^2 = 4x \). The parabola is symmetric about the x-axis. This means that if you have a point \( (x, y) \) on the parabola, the point \( (x, -y) \) will also be on the parabola. **Hint:** Remember that the symmetry of the parabola can help in identifying points related to each other. ### Step 2: Identify the given points ...
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