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A normal is drawn at a point P(x , y) of...

A normal is drawn at a point `P(x , y)` of a curve. It meets the x-axis at `Qdot` If `P Q` has constant length `k ,` then show that the differential equation describing such curves is `y(dy)/(dx)=+-sqrt(k^2-y^2)` . Find the equation of such a curve passing through `(0, k)dot`

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To solve the problem, we need to derive the differential equation for the curve based on the given conditions and then find the specific curve that passes through the point (0, k). ### Step-by-Step Solution: 1. **Understanding the Normal Line**: The normal to the curve at point \( P(x, y) \) can be expressed using the slope of the tangent. If \( \frac{dy}{dx} \) is the slope of the tangent, then the slope of the normal is \( -\frac{dx}{dy} \). The equation of the normal line at point \( P \) is given by: \[ y - y_1 = -\frac{dx}{dy}(x - x_1) ...
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