Question

If the vertices of a hyperbola be at $(-2,0)$ and $(2,0)$ and one of its foci be at $(-3,0),$ then which one of the following points does not lie on this hyperbola

• A. $(4,\sqrt{15})$
• B. $(2\sqrt{6},5)$
• C. $(6,5\sqrt{2})$
• D. $(-6,2\sqrt{10})$

Answer 1

The correct option is C $(6,5\sqrt{2})$

Let the equation of the hyperbola is
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
given
$a=2,ae=3$
As, $(ae{)}^2=a^2+b^2$
$\Rightarrow 9=4+b^2$
$\Rightarrow b^2=5$
$\therefore$ Equation of Hyperbola is
$\frac{x^2}{4}-\frac{y^2}{5}=1$
On sustituting the coordinates of all the points given in options, we can say that only the point $(6,5\sqrt{2})$ does not satisfy the equation of hyperbola.