JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q78

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MathematicsSingle correct+4 / -1Question 78 of 90

If a variable line drawn through the intersection of the lines $\dfrac x3+\dfrac y4=1$ and $\dfrac x4+\dfrac y3=1$ , meets the coordinate axes at A and B, (A ≠ B), then the locus of the midpoint of AB is :

6xy = 7(x + y)

4(x+y)^2-28(x+y)+49=0

7xy = 6(x + y)

14(x+y)^2-97(x+y)+168=0

Answer and worked solution

Official answer: C

The lines meet at $\left(\frac{12}7,\frac{12}7\right)$ . A line through it with intercepts 2h and 2k satisfies $\frac{12}{14h}+\frac{12}{14k}=1$ , i.e. $7hk=6(h+k)$ : the locus is $7xy=6(x+y)$ .

Topics:Locus Family of lines and pair of lines

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 78