If a variable line drawn through the intersection of the lines x 3 + y 4 = 1 and x 4 + y 3 = 1 , meets the coordinate axes at A and B , A   ≠ B , then the locus of the midpoint of AB is:

Question

If a variable line drawn through the intersection of the lines x 3 + y 4 = 1 and x 4 + y 3 = 1 , meets the coordinate axes at A and B , A &#160; &#8800; B , then the locus of the midpoint of AB is:

Aicharya · Accepted Answer

L 1 &#160; : 4 x + 3 y - 12 = 0 L 2 : 3 x + 4 y - 12 = 0 L 1 + &#955; L 2 = 0 &#8658; 4 x + 3 y - 12 + &#955; 3 x + 4 y - 12 = 0 &#8658; x 4 + 3 &#955; + y 3 + 4 &#955; - 12 1 + &#955; = 0 Point A 12 1 + &#955; 4 + 3 &#955; , &#160; 0 Point B 0 , 12 1 + &#955; 3 + 4 &#955; Mid point &#8658; h = 6 1 + &#955; 4 + 3 &#955; ....... i k = 6 1 + &#955; 3 + 4 &#955; ....... ii Eliminate &#955; from equations i and ii then 6 h + k = &#160; 7 h k Hence, locus is 6 x + y = &#160; 7 x y

If a variable line drawn through the intersection of the lines x 3 + y 4 = 1 and x 4 + y 3 = 1 , meets the…

Solution