The angle between the pair of tangents drawn to the ellipse $3x^2 + 2y^2 = 5$ from the point $(1, 2)$ is $\tan^{-1}\left(\frac{4}{5}\right)$, then the value of $\lambda$ is
Step-by-Step Solution
Key Concept: The distance from the origin to a point is found using the Pythagorean distance formula applied to the coordinates.
We have the reciprocal equation $\frac{1}{-1} = \frac{1}{1} = \frac{1}{-1}$, which shows the relationship between the values. The center is at $(h, k) = \left(-\frac{3}{5}, -\frac{1}{4}\right)$ for the ellipse. Using the distance formula, $OP = \sqrt{\left(-\frac{3}{5}\right)^2 + \left(-\frac{1}{4}\right)^2} = \sqrt{\frac{9}{25} + \frac{1}{16}}$. Converting to a common denominator: $\frac{9}{25} + \frac{1}{16} = \frac{144 + 25}{400} = \frac{169}{400}$. Therefore $OP = \frac{13}{20}$ units.
Correct Answer: 5