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Find the locus of the point of intersection of the lines, (root 2)x-y+4(root2)k=0 and (root2)kx+ky-4(root 2)k=0 ( k is any non-zero real parameter) is?

Find the locus of the point of intersection of the lines, (root 2)x-y+4(root2)k=0 and (root2)kx+ky-4(root 2)k=0 ( k is any non-zero real parameter) is?
 

Grade:12

1 Answers

Samyak Jain
333 Points
2 years ago
Equation of first line : \sqrt{2} x – y + 4\sqrt{2} k = 0    ….(1) and equation of second line : \sqrt{2} k x – k y + 4\sqrt{2} k = 0  i.e.
\sqrt{2} x + y – 4\sqrt{2} = 0      ….(2).
First equation represents parallel lines with constant slope (\sqrt{2}) but varying intercept as k is parameter.
When these lines will intersect the second given line, the locus of point of intersection is nothing but the second line.
Hence required equation of locus is \sqrt{2} x + y – 4\sqrt{2} = 0.

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