Find the locus of the point of intersection of tangents in the parabola `x^2=4a xdot` which are inclined at an angle `theta` to each other. Which intercept constant length `c` on the tangent at the vertex. such that the area of ` A B R` is constant `c ,` where `Aa n dB` are the points of intersection of tangents with the y-axis and `R` is a point of intersection of tangents.

Explanation

To find the locus of the point of intersection of tangents to the parabola \( x^2 = 4ay \) that are inclined at an angle \( \theta \) to each other and intercept a constant length \( c \) on the tangent at the vertex, we can follow these steps:

### Step 1: Equation of the Tangent
The equation of the tangent to the parabola \( x^2 = 4ay \) at a point \( (at^2, 2at) \) is given by:
\[ y = tx - at^2 \]
where \( t \) is the parameter corresponding to the point of tangency.
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