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  • Find the locus of the point of intersection of perpendicular tangents to the circles <img alt="\mathrm{x^2+y^2=a^2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&

Find the locus of the point of intersection of perpendicular tangents to the circles \mathrm{x^2+y^2=a^2}and \mathrm{x^2+y^2=b^2}

Option: 1

\mathrm{x^{2}-y^{2}=a^{2}+b^{2}}


Option: 2

\mathrm{x^{2}-y^{2}=a^{2}-b^{2}}


Option: 3

\mathrm{x^{2}+y^{2}=a^{2}+b^{2}}


Option: 4

\mathrm{x^{2}+y^{2}=a^{2}-b^{2}}


Answers (1)

best_answer

Any tangent to \mathrm{x^{2}+y^{2}=a^{2}} is 

x cos α + y sin α = a … (1) 

Any tangent to \mathrm{x^{2}+y^{2}=b^{2}} and perpdicular to (1) is 

x sin α − y cos α = b … (2) 

\mathrm{(1)^{2}+(2)^{2}x^{2}+y^{2}=a^{2}+b^{}}

which is the required locus.

 

Posted by

Rakesh

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