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P is any point of ellipse b2x2+a2y2=a2b2. Q is the foot of perpendicular from the centre to the tangent at P. As P moves around the ellipse,Q moves on the curve given by ----

P is any point of ellipse b2x2+a2y2=a2b2. Q is the foot of perpendicular from the centre to the tangent at P. As P moves around the ellipse,Q moves on the curve given by ----

Grade:12

2 Answers

TEJAS shah
16 Points
9 years ago

x2 + y2 = a2

Sarthak Chaturvedi
18 Points
9 years ago

Eqn. of ellipse: x^2/a^2 + y^2/b^2=1

Eqn.of tangent at P: xcosΘ/a + ysinΘ/b=1

Eqn.of perpendicular from centre to tangent: y=(atanΘ/b)x

Coordinates of foot of  perpendicular Q (ab2cosΘ/a2sin2Θ+b2cos2Θ,a2bsinΘ/a2sin2Θ+b2cos2Θ)

Locus of Q: x2+y2=a2b2

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