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Question
If an ellipse slides between two perpendicular straight lines, then the locus of its centre is
If an ellipse slides between two perpendicular straight lines, then the locus of its centre is
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Solution
The correct option is D a circle
Let 2a,2b be the length of the major and minor axes respectively of the ellipse. If the ellipse slides between two perpendicular lines, the
point of intersection P of these lines being the point of intersection
of perpendicular tangents lies on the Director circle of the ellipse.
This means that the centre C of the ellipse is always at a constant
distance √a2+b2 from P. Hence the locus of C is a
circle.
Let 2a,2b be the length of the major and minor axes respectively
of the ellipse. If the ellipse slides between two perpendicular lines, the
point of intersection P of these lines being the point of intersection
of perpendicular tangents lies on the Director circle of the ellipse.
This means that the centre C of the ellipse is always at a constant
distance √a2+b2 from P. Hence the locus of C is a
circle.
point of intersection P of these lines being the point of intersection
of perpendicular tangents lies on the Director circle of the ellipse.
This means that the centre C of the ellipse is always at a constant
distance √a2+b2 from P. Hence the locus of C is a
circle.
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