CUET · MATHS · PYQ PAPER 2023
If the vectors \(\hat{i}-2 x \hat{j}+3 y \hat{k}\) and \(\hat{i}+2 x \hat{j}-3 y \hat{k}\) are perpendicular, then the locus of \((x, y)\) is:
- A a circle
- B an ellipse
- C a hyperbola
- D a parabola
Answer & Solution
Correct Answer
(B) an ellipse
Step-by-step Solution
Detailed explanation
\(( \hat{i}-2 x \hat{j}+3 y \hat{k} ) \cdot ( \hat{i}+2 x \hat{j}-3 y \hat{k} ) = 0\) \((1)(1) + (-2x)(2x) + (3y)(-3y) = 0\) \(1 - 4x^2 - 9y^2 = 0\) \(4x^2 + 9y^2 = 1\) The locus is an ellipse.
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