Find the curve for which the intercept cut off by a tangent on x-axis is equal to four times the ordinate of the point of contact.

Explanation

To find the curve for which the intercept cut off by a tangent on the x-axis is equal to four times the ordinate of the point of contact, we will follow these steps:

### Step 1: Set up the equation of the tangent
Let \( y = f(x) \) be the equation of the curve. The slope of the tangent at any point \( (x, y) \) is given by \( \frac{dy}{dx} \). The equation of the tangent line at the point \( (x_0, y_0) \) is:
\[ y - y_0 = \frac{dy}{dx}\bigg|_{(x_0, y_0)} (x - x_0) \]
Rearranging gives:
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