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AP EAMCET202124 Aug 2021Evening ShiftMathematicsDeterminantsActual

Let 0 a z and A= [ array ccc a & a & a-y a & a+x & a a & a & a array ] be a matrix. Then, equation det A=16 represents

Options

  1. Aa parabola
  2. Ba circle
  3. Can ellipse
  4. Da rectangular hyperbola

Correct answer

D. a rectangular hyperbola

Step-by-step solution

We have, det (A)= | array ccc a & a & a-y a & a+x & a a & a & a array | Apply C₁ C₁-C₃ det (A)= | array ccc y & a & a-y 0 & a+x & a 0 & a & a array | |A|=y (a^2+a x-a^2 ) |A|=a x y 16= axy [given det A=16 ] x y= a 16 which represent a rectangular hyperbola.

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