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Find the co-ordinate of center of …

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Find the co-ordinate of center of a circle passing through the points (6,-6) , (3,-7) & (3,3)

Posted by Manish Tiwari 4 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 10 months ago

Let O (x, y) is the point of the circle

if three given points A (3,-7) B (3,3) and C (6,-6)

we know distance between circumference and center is always same. i.e radius .

now,

{tex}OA^2=OB^2=OC^2{/tex}

{tex}OA^2=OB^2{/tex}

{tex}=>(x-3)^2+(y+7)^2=(x-3)^2+(y-3)^2{/tex}

{tex}=>(x-3)^2-(x-3)^2=(y-3)^2-(y+7)^2{/tex}
{tex} => 0=(2y+4)(3){/tex}

{tex}=> y= -2{/tex}

now again ,

{tex}OB^2=OC^2{/tex}

{tex}(x-3)^2+(y-3)^2=(x-6)^2+(y+6)^2{/tex}

put y=-2

{tex}=>(x-3)^2+(-2-3)^2=(x-6)^2+(-2+6)^2{/tex}

{tex}=>(x-3)^2-(x-6)^2=16-25{/tex}

{tex}=>(2x-9)(3)=-9{/tex}

{tex}=> 2x= -3+9=6{/tex}

=> x=3

hence center co-ordinate is (3,-2)

3Thank You

ANSWER

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CBSE > Class 10 > Mathematics