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Find the points of contact of vertical tangents to X =2-3sinα,Y=3+2cosα

Find the points of contact of vertical tangents to X =2-3sinα,Y=3+2cosα

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
sin alpha = (x – 2) / -3
 
cos alpha = (y – 3)/2
 
now
since sin^2 alpha + cos ^2 alpha = 1
 
hence
 
(x – 2)^2 / 9 + (y – 3)^2 / 4 = 1
 
this is an ellpise with centre at (2, 3) 
 
its vertex will be at 
 
(2 + 3 , 3) and (2 – 3, 3 )
 = (5, 3) and ( –1, 3)
 
which are also points of contact of vertical tangents

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