The intersection of two perpendicular tangent | vedclass

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Question

(A) The locus of the point of intersection of perpendicular tangents to a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is known as the director c

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The locus of the point of intersection of perpendicular tangents to a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is known as the director circle,given by the equation $x^2 + y^2 = a^2 - b^2$.For the given hyperbola $\frac{x^2}{4} - \frac{y^2}{2} = 1$,we have $a^2 = 4$ and $b^2 = 2$.Substituting these values into the director circle equation,we get $x^2 + y^2 = 4 - 2 = 2$.Thus,the intersection point lies on the circle $x^2 + y^2 = 2$.Hence,option $A$ is correct.

The intersection of two perpendicular tangents to the hyperbola $\frac{x^2}{4} - \frac{y^2}{2} = 1$ lies on the circle $x^2 + y^2 = \dots \dots \dots$

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