For the hyperbola $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{3} = 1$ the incorrect statement is :
For the hyperbola $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{3} = 1$ the incorrect statement is :
- A
product of the perpendicular distances from any point on the hyperbola on its asymptotes is less than the length of its latus rectum .
- B
its eccentricity is $4/3$
- C
length of the latus rectum is $2$
- D
both $(A)$ and $(B)$
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Let $0 < \theta < \frac{\pi }{2}$. If the eccentricity of the hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\,\theta }} - \frac{{{y^2}}}{{{{\sin }^2}\,\theta }} = 1$ is greater than $2$, then the length of its latus rectum lies in the interval
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lf $e_1$ , $e_2$ and $e_3$ are eccentricities of the conics $y = {x^2} - x + 3,\,\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{3{a^4}}} = 1$ and ${a^2}{x^2} - 3{a^4}{y^2} = 1$ respectively, then which of the following is correct ? (where $a > 1)$
lf $e_1$ , $e_2$ and $e_3$ are eccentricities of the conics $y = {x^2} - x + 3,\,\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{3{a^4}}} = 1$ and ${a^2}{x^2} - 3{a^4}{y^2} = 1$ respectively, then which of the following is correct ? (where $a > 1)$
Product of length of the perpendiculars drawn from foci on any tangent to hyperbola ${x^2} - \frac{{{y^2}}}{4}$ = $1$ is
Product of length of the perpendiculars drawn from foci on any tangent to hyperbola ${x^2} - \frac{{{y^2}}}{4}$ = $1$ is