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BITSAT2023MathematicsHyperbolaActual

The vertices of the hyperbola 9 x^2-16 y^2-36 x+96 y-252=0 are

Options

  1. A(6,3),(-2,3)
  2. B(6,3),(-6,3)
  3. C(-6,3),(-6,-3)
  4. D(2,3),(-2,3)

Correct answer

A. (6,3),(-2,3)

Step-by-step solution

Given hyperbola is aligned & 9 x^2-16 y^2-36 x+96 y-252=0 & 9 (x^2-4 x )-16 (y^2-6 y )=252 & 9 (x^2-4 x+4 )-16 (y^2-6 y+9 ) & =252+36-144 & 9(x-2)^2-16(y-3)^2=144 aligned Put x=X+2 and y=Y+3 Equation (i) becomes X^2 16 - Y^2 9 =1 Now, vertices are X= a wehre a=4 and Y=0 Hence, vertices are (6,3),(-2,3) .

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