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STD 11 - 10.2 parabola,ellipse,hyperbola — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.2 parabola,ellipse,hyperbola4 Marks
MCQ
The equation $\frac{{{x^2}}}{{29 - p}}$ $+ $$\frac{{{y^2}}}{{4 - p}}$ $= 1$  $(p  \ne 4, 29)$ represents
  • A
    an ellipse if $p$  is any constant greater than $ 4.$ 
  • ✓
    a hyperbola if $  p $ is any constant between $4$ and $29.$
  • C
    a rectangular hyperbola if $p$ is any constant greater than $29$.
  • D
    no real curve if $p$ is less than $ 29.$ 
✓

Answer

Correct option: B.
a hyperbola if $  p $ is any constant between $4$ and $29.$
b
Equation of Hyperbola is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

if p lies between 4 and 29 then coefficient of $y^{2}$ is negative and coefficient of $x^{2}$ is positive

Hence, it satisfies the equation of Hyperbola between 4 and 29

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