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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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Find the equation of straight line touching both $x^2+y^2=2$ and $y^2=8x$.

$\begin{array}{1 1}(a)\;x\pm y+2=0\\(b)\;x\pm 2y+2=0\\(c)\;x\pm y+3=0\\(d)\;x\pm y+12=0\end{array}$

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For the parabola $y^2=8x$
Equation of tangent in slope form for parabola
We know if this is the common tangent that it will pass through circle hence its distance from the centre of circle will be its radius hence
Squaring $\large\frac{\Large\frac{4}{m^2}}{1+m^2}$$=2$
$m^2+2\neq 0$
$m=\pm 1$
Hence the required tangents are $x\pm y+ 2=0$
Hence (a) is the correct answer.
answered Feb 5, 2014 by sreemathi.v
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