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No. Of the distinct normals that can be drawn to the ellipse x^2/169+y^2/25=1 from point p(0,6) is?

No. Of the distinct normals that can be drawn to the ellipse x^2/169+y^2/25=1 from point p(0,6) is?

Grade:11

2 Answers

deepak
12 Points
3 years ago
equation of normal at point:(13cos∅,5sin∅) is
13x/cos∅ - 5y/sin∅=144
it passes through (0,6),therefore;
(15+72sin∅=0) or (sin∅=-5/24)
OR
∅=2π-sin^-1(5/24) & π+sin^-1(5/24)
hence,y axis is also one of the normals.
deepak
12 Points
3 years ago
equation of normal at point can be written as ax/cos∅ - by/sin∅ = (ae)^2
where e is eccentricity,a=13,b=5
therefore equation of normal is
13x/cos∅ - 5y/sin∅=144
it passes through (0,6),therefore;
(15+72sin∅=0) or (sin∅=-5/24)
therefore there is 2 values of sin∅ which corresponds to 2 normals
∅ = 2π - sin^-1(5/24) &
∅ = π + sin^-1(5/24)
also y axis is also one of the normals.
therefore total 3 normals can be drawn

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