The equation of the normal of slope m to the hyperbola
x2a2−y2b2=1
is given by y=mx±m(a2+b2)√a2−b2m2
True
We already know that equation of normal at a point (x1,y1) is given by,
a2xx1+b2yy1=a2+b2
If m is the slope of normal, at (x1,y1)
then m=−a2y1b2x1
since (x1,y1) lies on x2a2−y2b2=1
putting the value of y1 in the equation
we get,
x1=±a2√a2−b2m2
y1=±b2m√a2−b2m2
∴ On giving these values in the equation
a2xx1+b2yy1=a2+b2 we get
y=mx±m(a2+b2)√a2−b2m2
as the equation of normal at the point
(±a2√a2−b2m2,±b2m√a2−b2m2)