Question

If the vectors $2x\hat{i}-y\hat{j}-4\hat{k}$ and $10\hat{i}+\hat{y}+5\hat{k}$ are perpendicular, then the locus of $(x,y)$ is

• A. A Parabola with vertex at $(1,0)$ and latus rectum $10$
• B. A Parabola with vertex at $(0,1)$ and latus rectum $20$
• C. A Parabola with vertex at $(1,0)$ and latus rectum $20$
• D. A Parabola with vertex at $(0,1)$ and latus rectum $10$

Answer 1

Answer: (C)

A Parabola with vertex at $(1,0)$ and latus rectum $20$

Since Vectors are perpendicular, then taking Dot product

$(2x\overline{i}-y\overline{j}-y\overline{k})\cdot (10\overline{i}+y\overline{j}+5\overline{k})=0$
$=20x-y^2-20=0$
$y^2=20(x-1)$

A Parabola with vertex $(1,0)$ and latus rectum $20$.