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Find the llocus of the points of the int...

Find the llocus of the points of the intersection of tangents to ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` which make an angle 0.

A

parabola

B

circle

C

ellipse

D

straight line

Text Solution

Verified by Experts

As in the above equstion, the points of intersection is `(h,k)-=(-cos((alpha+beta)/(2))/(cos((alpha-beta)/(2))),-(bsin((alpha+beta)/(2)))/(cos.((alpha-beta)/(2))))`
It is given that `alpha+beta=c` = constant, Therefore,
`h=-(acos.(c)/(2))/(cos.((alpha-beta)/(2)) ) and k=-(bsin.(c)/(2))/(cos.((alpha-beta)/(2)))`
or `(h)/(k)=(a)/(b)cot.((c)/(2))`
`or k=(b)/(a)tan.((c)/(2))h`
Therefore, (h,k) lies on the straight line
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