Grade 12th passAnalytical Geometry
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
