find the locus of a point equidistant from the lines x+y+4=0 and 7x+y+20=0.

Let the points be h, k and the two lines are, x+y+4=0 and 7x+y+20-0Now according to the question, a1x1+b1y1+c1a12+b12=a2x1+b2y1+c2a22+b22Here x1=h, y1=kSo we get, h+k+71+1=7h+k+2049+1squaring we get, 25h+k+72=7h+k+20225h2+25k2+1225+50hk+350k+350h=49h2+k2+400+14hk+40k+280h24h2-24k2-825-36hk-310k-70h=0Putting x=h, k=y we get, 24x2-24y2-36xy-70x-310y-825=0and it is a eqaution of hyperbola.

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