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what is the condition for the line xcos(alpha)+ysin(alpha) =p to be tangent to the ellipse x^2/A^2+y^2/B^2=1

what is the condition for the line xcos(alpha)+ysin(alpha) =p to be tangent to the ellipse x^2/A^2+y^2/B^2=1

Grade:12

1 Answers

neena
111 Points
8 years ago
for this line to represent a tangent to the ellipse it should satisfy the condition for tangency of an arbitary line y=mx+c and ellipse that is c^2=a^2*m^2+b^2 hence when we put the values of all the related terms we get the condition as p^2=a^2cos^2(\alpha)+b^2sin^2(\alpha). 

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