Question:
The locus of the point of intersection of the lines
\[
x = \frac{1 - t^2}{1 + t^2}, \quad y = \frac{2 a t}{1 + t^2}
\]
represents:
The locus of the point of intersection of the lines
\[ x = \frac{1 - t^2}{1 + t^2}, \quad y = \frac{2 a t}{1 + t^2} \]
represents:
\[ x = \frac{1 - t^2}{1 + t^2}, \quad y = \frac{2 a t}{1 + t^2} \]
represents:
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Parametric forms often reduce to standard conics.
Updated On: Mar 23, 2026
- circle
- parabola
- ellipse
- hyperbola
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The Correct Option is C
Solution and Explanation
Step 1: Eliminate \(t\):
\[ x^2 + \frac{y^2}{a^2} = 1 \]
Step 2: This is the standard equation of an ellipse.
\[ x^2 + \frac{y^2}{a^2} = 1 \]
Step 2: This is the standard equation of an ellipse.
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