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Grade 12Analytical Geometry

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?

nitin ticroliya

7 Years agoGrade 12

1 Answer

Samyak Jain

7 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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