Question

The number of points (a, b), (a ,b, $ϵI$) In the x - y plane from where to mutually perpendicular tangents can be drawn to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$ is

• A. 1
• B. 2
• C. 4
• D. infinite

Answer 1

The correct option is C 4

Point (a , b)must lie on the director circle
$x^2+y^2$ = 16
$\therefore$ Number of points (a , b) on the circle whose abscissa and ordinate both are integers are 4
i.e(4,0)(0,4)(-4,0)(0,-4).