Ellipse
Semi-minor axis from tangent line condition
MJAT_TS4_P1
Grade 12
Question:
$y=x$ is tangent to an ellipse having foci at $(2,3)$ and $(5,7)$. The length of the semi-minor axis of the given ellipse is:
Step-by-Step Solution
Key Concept: For a tangent to an ellipse with foci $F_1$ and $F_2$: the tangent is the external bisector of $\angle F_1PF_2$ at the point of tangency. The reflection of one focus in the tangent line must lie on the line joining the other focus and the tangent point.
Semi-minor axis $b=\mathbf{1}$.
Correct Answer: 1