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Normal at point P(x1,y1), not lying on x...

Normal at point `P(x_1,y_1)`, not lying on x-axis, to the hyperbola `x^2-y^2=a^2` meets x-axis at A and y-axis at B. If O is origin then:

A

Circumcentre of triangle OAB at P

B

Slope of OP + slope of AB = 0

C

Slope of OP = slope of AB

D

Locus of centroid of triangle OAB is a rectangular hyperbola

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The correct Answer is:
A, B, D
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