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  • If the circles <img alt="\mathrm{x^2+y^2+2 x+2 k y+6=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2&plus;2%20x&plus;2%20k%20y&plus;6%3D0%7D" /

If the circles \mathrm{x^2+y^2+2 x+2 k y+6=0} and \mathrm{x^2+y^2+2 k y+k=0} intersect orthogonally, the k is
 

Option: 1

2\text{ or }\frac{-3}{2}


Option: 2

-2\text{ or }\frac{-3}{2}


Option: 3

2\text{ or }\frac{3}{2}


Option: 4

-2\text{ or }\frac{3}{2}


Answers (1)

best_answer

\begin{aligned} &\mathrm{ (1) (0)+2(k)=k+6}\\ &\mathrm{or \ 2 k^2-k-6=0}\\ &\mathrm{or \ 2 k^2-4 k+3 k-6=0}\\ &\mathrm{or\ k=\frac{-3}{2},+2} \end{aligned}

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