Question

# If rectangular hyperbola $$x^{2}- y^{2} = 4$$ is converted to $$xy = -c^{2}$$, then the equation of tangent to the hyperbola $$xy =- c^{2}$$ at point $$t, t$$ being a parameter, is :

A
xt+yt=±2
B
xt+yt±42=0
C
xtyt±22=0
D
xtyt±42=0

Solution

## The correct option is C $$\dfrac{x}{t}-yt\pm 2\sqrt{2} =0$$$$x^2-y^2=a^2$$ is converted into $$xy=-\dfrac{a^2}{2}$$, if axis is rotated by $$45^\circ$$ in clockwise direction. So in given equation,$$c^2=\dfrac{a^2}{2}=\dfrac{4}{2}=2$$$$c=\pm \sqrt2$$Any parametric point on hyperbola $$=\left(ct,\dfrac{-c}{t}\right)$$Equation of tangent $$xct-y\dfrac{c}{t}=-2c^2$$$$\Rightarrow xt-\dfrac{y}{t}=-2c$$$$\Rightarrow xt-\dfrac{y}{t}\pm 2\sqrt2=0$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More