Question
The vertices of the hyperbola 9 x^2-16 y^2-36 x+96 y-252=0 are
BITSAT
Mathematics
Hyperbola
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. (6,3),(-2,3)
- B. (6,3),(-6,3)
- C. (-6,3),(-6,-3)
- D. (2,3),(-2,3)
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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