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The locus of the point (h,k) for which t...

The locus of the point `(h,k)` for which the line `hx+ky=1` touches the circle `x^2+y^2=4`

Text Solution

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`x=sqrt(3)((1-t^(2))/(1+t^(2))),y=(2t)/(1+t^(2))`
Let `t= tan alpha`
`:.cos 2alpha=(x)/(sqrt(3)) and sin 2alpha=y`
`:. (x^(2))/(3)+y^(2)=sin^(2)2alpha+cos^(2)2alpha=1`
Note : Solutions of the remainnig parts are given in their respective chapters.
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