Let be a point with integer coordinates from which the two tangents to the ellipse are perpendicular to each other. How many such points are there?
Answer and explanation
Correct answer: B. 12
- Step 1: The locus of points from which mutually perpendicular tangents can be drawn to an ellipse is its director circle, given by .
- Step 2: For the given ellipse, and , which gives the director circle equation .
- Step 3: Find all integer pairs satisfying : the axial points and , plus the non-axial points and . The total number of points is .
Answer
12.
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