Question

Length of the semi-transverse axis of the rectangular hyperbola xy=8 is

Answer 1

√8 = 2√2..........



...

Answer 2

Answer:

The length of  semi-transverse axis of the rectangular hyperbola xy=8 is 4 units.

Step-by-step explanation:

The equation of the rectangular hyperbola is

$xy=8$

The vertex of the rectangular hyperbola lie on the line y=x.

First of all find the vertex of the rectangular hyperbola,

Put y=x in the given equation.

$x\times x=8$

$x^2=8$

$x=\pm 2\sqrt{2}$

The value of x is $\pm 2\sqrt{2}$, so the vale of y is $\pm 2\sqrt{2}$.

Length of the transverse axis is the distance between $(2\sqrt{2},2\sqrt{2})$ and $(-2\sqrt{2},-2\sqrt{2})$.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$D=\sqrt{(-2\sqrt{2}-2\sqrt{2})^2+(-2\sqrt{2}-2\sqrt{2})^2}$

$D=\sqrt{(-4\sqrt{2})^2+(-4\sqrt{2})^2}$

$D=\sqrt{32+32}$

$D=\sqrt{64}$

$D=8$

The length of transverse axis is 8. The length of semi transverse axis is half of length of transverse axis.

$\frac{8}{2}=4$

Therefore the length of  semi-transverse axis of the rectangular hyperbola xy=8 is 4 units.