Q. 144.8( 4 Votes )

Find the point on

Answer :

Given:


The curve x2 + y2 = 13 and the line 2x + 3y = 7


x2 + y2 = 13


Differentiating the above w.r.t x


2x2 – 1 + 2y2 – 1 = 0


2x + 2y = 0


2(x + y) = 0


(x + y) = 0


y = – x


...(1)


Since, line is 2x + 3y = 7


3y = – 2x + 7


y =


y = +


The equation of a straight line is y = mx + c, where m is the The Slope of the line.


Thus, the The Slope of the line is ...(2)


Since, tangent is parallel to the line,


the The Slope of the tangent = The Slope of the normal


=


– x =


x =


Substituting x = in x2 + y2 = 13,


()2 + y2 = 13


() + y2 = 13


y2() = 13


y2() = 13


y2() = 1


y2 = 9


y = 3


Substituting y = 3 in x = ,we get,


x =


x = 2


Thus, the required point is (2, 3) & ( – 2, – 3)


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