Find the equation of the line passing through the point (11,-2) and touching the circle x2+y2=25

Dear Student,
Please find below the solution to the asked query:

We havex2+y2=25x-02+y-02=52On comparing it with:x-h2+y-k2=r2We get Centreh,k=C0,0Radiusr=5 unitsLet required equation of line be:mx-y+c=0Line passes through 11,-211m--2+c=011m+2+c=0c=-11m-2mx-y+c=0 becomesmx-y-11m-2=0As line touches circle hence length of perpendicular from center of circleto line will be equal to radius of circle.0-0-11m-2m2+-12=5-11m+2m2+1=5Squaring both sides we get,11m+221+m2=25121m2+4+44m=25+25m2121m2-25m2+44m+4-25=096m2+44m-21=096m2+72m-28m-21=024m4m+3-74m+3=024m-74m+3=0m=724 or m=-34We have mx-y-11m-2=0When m=7247x24-y-7724-2=07x-24y-77-4824=07x-24y-125=0When m=-34-3x4-y+334-2=0Multiply both sides by -4,3x+4y-33+8=03x+4y-25=0

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • -1
= 150 ??
I don't know but my answer may be correct !!
  • 0
What are you looking for?