Parabola
Tangent and Chord of Contact
Grade 11
Question:
<p>Tangents are drawn to the parabola <span>\(y = -\frac{x^2}{4}\)</span>. If the chord of contact passes through the point <span>\((0, 1)\)</span> which lies on the directrix <span>\(y = 1\)</span>, find the number of points required.</p>
Step-by-Step Solution
Key Concept: The chord of contact from a point on the directrix intersects the parabola at specific points determined by the tangent conditions.
<p><strong>Solution:</strong></p><p>For parabola <span>\(y = -\frac{x^2}{4}\)</span>, the directrix is <span>\(y = 1\)</span>.</p><p>Points lie on directrix <span>\(y = 1\)</span>.</p><p>The points required are the intersection of the chord of contact lines <span>\(\frac{x}{4} + \frac{y}{3} = \frac{1}{2}\)</span> and <span>\(y = 1\)</span>.</p><p>∴ Number of points required = <strong>1</strong></p>
Correct Answer: 1