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Question

The equation of the normal of slope m to the hyperbola
x2a2y2b2=1
is given by y=mx±m(a2+b2)a2b2m2


A

True

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B

False

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Solution

The correct option is A

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 x2a2y2b2=1

putting the value of y1 in the equation

we get,

x1=±a2a2b2m2

y1=±b2ma2b2m2

On giving these values in the equation

a2xx1+b2yy1=a2+b2 we get

y=mx±m(a2+b2)a2b2m2
as the equation of normal at the point
(±a2a2b2m2,±b2ma2b2m2)


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