Q. 224.7( 3 Votes )
Find the point on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to the y – axis. (CBSE 2011)
Answer :
Since, the tangent is parallel to y – axis, its slope is not defined, then the normal is parallel to x – axis whose slope is zero.
i.e,
= 0
⇒ 
= 0
⇒ 
= 0
⇒ y = 0
Substituting y = 0 in x2 + y2 – 2x – 3 = 0,
x2 + 02 – 2×x – 3 = 0
x2 – 2x – 3 = 0
Using factorization method, we can solve above quadratic equation
x2 – 3x + x – 3 = 0
x(x – 3) + 1(x – 3) = 0
(x – 3)(x + 1) = 0
⇒ x = 3 & x = – 1
Thus, the required point is (3,0) & ( – 1,0)
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