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Analytical Geometry

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Joined:	3 Oct 2009
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15 Oct 2009 00:23:29 IST

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find the range of parameter a fr which the variable line y=2x+a lies btw the circle x(sqr)+y(sqr

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find the range of parameter a fr which the variable line y=2x+a lies btw the circle x(sqr)+y(sqr)-2x-2y+1=0 &x(sqr)+y(sqr)-16x-2y+61=0 widout touching or intersecting either circle

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kabi

Blazing goIITian

Joined: 11 Jan 2009

Posts: 575

16 Oct 2009 00:53:07 IST

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hello

i m not going to solve this prob just giving the approach

first of all draw the circles so that u can actually visualise where a should lie .

we want y = 2x+a neither to touch the circles nor intersect any of them

put y = 2x +a in the eq. x²+y²-2x-2y+1 =0

u will get

5x² +4xa -6x+a² -2a +1 =0

for fulfilling the condition we want the d < 0 of this quadractic

so a²+2a -4 >0

solve this a >sqrt(5)-1 or a < - (sqrt(5)+1)

if we want such value of a so that lie b/w the circles u can easily come to conclusion

we want a < - (sqrt(5)+1) only .

then do the same thing for second circle . and find the value of a . ask me again if u have prob.

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