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Find the equation of circle having x-y-2=0 and x-y+2=0 as two tangents and x-y=0as diameter?(ans is x 2 + y 2 =2)how??????

Find the equation of circle having x-y-2=0 and x-y+2=0 as two tangents and x-y=0as diameter?(ans is   x2 + y2 =2)how??????



Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear   arzoo

given tangent line and diameter line are parallel to each other

radius is equal to distance between ant tangent line and diameter line that is equal to = √2

and center of line lie on the line the diameter line/

let co ordinate of center is (h,k)

since this lie on line x-y=0

so h=k

so equation of circle  (x-h)2 +( y-h)2 =2

it is a family of circle one of the possible circle is for h=0

 x2 + y2 =2

similerly you will get many nore circle for different value of h

I think equation of diameter line should be x+y=0

then you will onle one circle  x2 + y2 =2



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Badiuddin



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