Let the values of p, for which the shortest distance between the lines (x+1)/3=y/4=z/5 and r=(pi+2j+k)+λ(2i+3j+4k) is 1/(6), be a,b with a<b. Then the length of the latus rectum of the ellipse (x²)/(a²)+(y²)/(b²)=1 is:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q106

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

Let the values of

p

, for which the shortest distance between the lines

\displaystyle\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5}

and

\mathbf{r}=(p\hat{i}+2\hat{j}+\hat{k})+\lambda(2\hat{i}+3\hat{j}+4\hat{k})

\tfrac{1}{\sqrt6}

, be

a,b

with

a<b

. Then the length of the latus rectum of the ellipse

\displaystyle\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

is: