document.write( "Question 967614: find an equation of a circle passing through the points A(1,2) and B(1,-2) and touching the line x+2y+5=0? \n" ); document.write( "

Algebra.Com's Answer #591398 by askhari139(3) $\"\"$ $\"About$

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To write the equation of any circle, you need a center and a radius. So, if (a,b) is the center and r is the radius of the circle, the circle equation would be
\n" ); document.write( " $\"%28x-a%29%5E2+%2B+%28y-b%29%5E2+=+r%5E2\"$
\n" ); document.write( "In this problem, you have 2 pieces of information. One, 2 points one the circle and two, a tangent. Let the coordinates of the center be O(a,b) and the radius be r.
\n" ); document.write( "Since point A and point B are points on the circle, distance between O and A will be equal to O and B which in turn would be equal to r.
\n" ); document.write( " OA = OB = r
\n" ); document.write( " => $\"sqrt%28%28a-1%29%5E2%2B%28b-2%29%5E2%29+=+r\"$ ....... (1)
\n" ); document.write( " $\"sqrt%28%28a-1%29%5E2%2B%28b-%28-2%29%29%5E2%29+=+r\"$ .... (2)
\n" ); document.write( "Also, since x+2y+5 = 0 touches the circle, it is a tangent to the circle. and hence, distance between centre O and the line will also be equal to r.
\n" ); document.write( " => $\"sqrt%28%28a%2B2b%2B5%29%2Fsqrt%281%5E2%2B2%5E2%29%29+=+r\"$ ......... (3)\r
\n" ); document.write( "\n" ); document.write( "For the 3 variables a,b,r, you have 3 equations. Solve them and you will get the answer.\r
\n" ); document.write( "\n" ); document.write( "message me if you have any further problems.
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