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A point moves such that the sum of the squares of its distances from two intersecting straight lines ​(need not be perpendicular) ​is constant. Prove that its locus is an ellipse and find the eccentricity in terms of angle between the straight lines. (Coordinate Geometry, SK Goyal, Ellipse) Ans. Eccentricity = √(1 – ​(cosecα + cotα) -2 ​), where α is the angle between the lines

A point moves such that the sum of the squares of its distances from two intersecting straight lines ​(need not be perpendicular) ​is constant. Prove that its locus is an ellipse and find the eccentricity in terms of angle between the straight lines.
 
(Coordinate Geometry, SK Goyal, Ellipse)
 
Ans. Eccentricity = √(1 – ​(cosecα + cotα)-2​), where α is the angle between the lines

Grade:12th pass

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