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)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?How to find Maxima & Minima?How to find Maxima & Minima?43 mins
Practise Questions - Application of DerivativesPractise Questions - Application of DerivativesPractise Questions - Application of Derivatives45 mins
Interactive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minimaInteractive quiz on maxima and minimaInteractive quiz on maxima and minima48 mins
Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)55 mins
Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)52 mins
Tangent & Normal To A CurveTangent & Normal To A CurveTangent & Normal To A Curve53 mins
Application of BiotechnologyApplication of BiotechnologyApplication of Biotechnology48 mins
Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 0256 mins
Application of Nerst EquationApplication of Nerst EquationApplication of Nerst Equation20 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses