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This is the question in my textbook--

Find the condition that the straight line $cx - by +b^2 = 0$ may touch the circle $x^2 + y^2 = ax + by $?

My approach:- I made the distance of the center of the circle from the line to be equal to the radius of the circle in which the line will just touch the circle but i am going no were

can anyone tell me what do any help will be helpful

Thank's

Akash

Deiknymi
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  • The approach you described should work. The condition is: distance from line to circle center = radius of circle. The rest is just algebra. – bubba Oct 12 '13 at 04:45

1 Answers1

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If you solve for $y$ in your equation of a line, you can plug that into the equation of the circle. You will then have a single variable, namely $x$. Solve for it; you will need the quadratic formula. For certain $a,b,c$ there will be no solutions, or two. What you want is a single solution, a single possible value for $x$. So long as your line isn't vertical (i.e. $b\neq 0$), the line will then be tangent to the circle.

vadim123
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