JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 75

If a straight line drawn through the point of intersection of the lines $4x+3y-1=0$ and $3x+4y-1=0$ , meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is :

x+y-7=0

x+y-14xy=0

2x+y+14xy=0

x+2y-14xy=0

Answer and worked solution

Official answer: B

Intersection. $4x+3y=1$ and $3x+4y=1$ meet at $\left(\tfrac17,\tfrac17\right)$ .

Line through it. With midpoint $(h,k)$ , the intercepts are $2h$ and $2k$ :
$\frac{1/7}{2h}+\frac{1/7}{2k}=1\ \Rightarrow\ h+k=14hk.$

Locus: $x+y-14xy=0$ .

(B)

Topics:Locus Family of lines and pair of lines

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 10