Ellipse
Tangent to Ellipse
Grade 11
Question:
<p>Let \(d\) be the perpendicular distance from the centre of the ellipse to any tangent to the ellipse. If \(F_1\) and \(F_2\) are the two foci of the ellipse, then</p>
<p>(a) \((PF_1 + PF_2)^2 = a^2\left(1 + \frac{b^2}{d^2}\right)\)</p>
<p>(b) \((PF_1 + PF_2)^2 = \frac{4a^2b^2}{d^2}\)</p>
<p>(c) \((PF_1 - PF_2)^2 = 4a^2\left(1 - \frac{b^2}{d^2}\right)\)</p>
<p>(d) \((PF_1 - PF_2)^2 = a^2\left(1 + \frac{d^2}{b^2}\right)\)</p>
Step-by-Step Solution
Key Concept: Relate the distance from center to tangent with the focal radii using properties of ellipse tangents.
<p>Solution not provided in text.</p>
Correct Answer: C