Answer :

Given:


The curve is y = 3x2 – 9x + 8


Differentiating the above w.r.t x


y = 3x2 – 9x + 8


= 23x2 – 1 – 9 + 0


= 6x – 9 ...(1)


Since, the tangent are equally inclined with axes


i.e, or


= The Slope of the tangent = tan


= tan() or tan()


= 1or – 1 ...(2)


tan() = 1


From (1) & (2),we get,


6x – 9 = 1 0r 6x – 9 = – 1


6x = 10 0r 6x = 8


x = or x =


x = or x =


Substituting x = or x = in y = 3x2 – 9x + 8,we get,


When x =


y = 3()2 – 9() + 8


y = 3() – () + 8


y = () – () + 8


taking LCM = 9


y = ()


y = ()


y = ()


y = ()


when x =


y = 3()2 – 9() + 8


y = 3() – () + 8


y = () – () + 8


taking LCM = 9


y = ()


y = ()


y = ()


y = ()


Thus, the required point is (,) & (,)


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