Foci of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{{(y - 2)}^2}}}{9} = 1$ are
Foci of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{{(y - 2)}^2}}}{9} = 1$ are
- A
$(5, 2) (-5, 2)$
- B
$(5, 2) (5, -2)$
- C
$(5, 2) (-5, -2)$
- D
None of these
Similar Questions
If $2 x-y+1=0$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following $CANNOT$ be sides of a right angled triangle?
$[A]$ $2 a, 4,1$ $[B]$ $2 a, 8,1$ $[C]$ $a, 4,1$ $[D]$ $a, 4,2$
If $2 x-y+1=0$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following $CANNOT$ be sides of a right angled triangle?
$[A]$ $2 a, 4,1$ $[B]$ $2 a, 8,1$ $[C]$ $a, 4,1$ $[D]$ $a, 4,2$
- [IIT 2017]
The point of contact of the line $y = x - 1$ with $3{x^2} - 4{y^2} = 12$ is
The point of contact of the line $y = x - 1$ with $3{x^2} - 4{y^2} = 12$ is
The eccentricity of the hyperbola $4{x^2} - 9{y^2} = 16$, is
The eccentricity of the hyperbola $4{x^2} - 9{y^2} = 16$, is
The foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the hyperbola $\frac{{{x^2}}}{{144}} - \frac{{{y^2}}}{{81}} = \frac{1}{{25}}$ coincide. Then the value of $b^2$ is
The foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the hyperbola $\frac{{{x^2}}}{{144}} - \frac{{{y^2}}}{{81}} = \frac{1}{{25}}$ coincide. Then the value of $b^2$ is
The minimum value of ${\left( {{x_1} - {x_2}} \right)^2} + {\left( {\sqrt {2 - x_1^2} - \frac{9}{{{x_2}}}} \right)^2}$ where ${x_1} \in \left( {0,\sqrt 2 } \right)$ and ${x_2} \in {R^ + }$.
The minimum value of ${\left( {{x_1} - {x_2}} \right)^2} + {\left( {\sqrt {2 - x_1^2} - \frac{9}{{{x_2}}}} \right)^2}$ where ${x_1} \in \left( {0,\sqrt 2 } \right)$ and ${x_2} \in {R^ + }$.