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  • Through a fixed point (h, k), secants are drawn to the circle<img alt="\mathrm{x^{2}+y^{2}=r^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E%7

Through a fixed point (h, k), secants are drawn to the circle\mathrm{x^{2}+y^{2}=r^{2}}. Find the locus of the mid-points of the portions of the secants intercepted by the circle is \mathrm{x^{2}+y^{2}=hx+ky}. 

 

Option: 1

\mathrm{xh+ky=x^{2}-y^{2}}


Option: 2

\mathrm{xh-ky=x^{2}-y^{2}}


Option: 3

\mathrm{xh-ky=x^{2}+y^{2}}


Option: 4

\mathrm{xh+ky=x^{2}+y^{2}}


Answers (1)

best_answer

Equation of AB is \mathrm{T}=\mathrm{S}_1

\mathrm{i.e. \: x \alpha+y \beta-r^2=\alpha^2+\beta^2-r^2}

\mathrm{i.e. \: x \alpha+y \beta=a^2+\beta^2}

Since it passes through (h, k) we get

\mathrm{h \alpha+k \beta=\alpha^2+\beta^2}

⇒ Equation of locus is \mathrm{x h+y k=x^2+y^2}

 

 

Posted by

Ajit Kumar Dubey

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