Exams › JEE Main › Maths
For the curve defined by x² + y² = a², if k = 1/a, then k can be written as
- |y''| / √(1+y'²)
- |y''| / √((1+y'²)³)
- 2y'' / √(1+y'²)
- y'' / (2√((1+y'²)³))
Correct answer: |y''| / √((1+y'²)³)
Solution
The correct option expresses the curvature of the circle defined by the equation x² + y² = a² in terms of the second derivative of y, which relates to how the slope of the tangent line changes. The formula for curvature involves the second derivative and accounts for the slope's contribution to the curvature, hence the presence of the term (1+y'²) raised to the power of 3.
Related JEE Main Maths questions
- For the curve y² = 2x³, identify the point P at which the tangent is perpendicular to the line 4x - 3y + 2 = 0.
- For the function f(x) = 2x² - log|x|, with x ≠ 0, on which interval is the function increasing throughout?
- Two upright poles AP and BQ stand at points A and B respectively. If AP = 16 m, BQ = 22 m, and the distance AB = 20 m, then for a point R on AB, the value of AR for which RP² + RQ² is least is
- For the curve x⁴ + y⁴ = a⁴, a tangent drawn at an arbitrary point meets the coordinate axes at intercepts p and q. Then the quantity p^(-4/3) + q^(-4/3) equals
- A particle travels on the curve y = x³ + 2. Find the point(s) P on the curve where the y-coordinate changes at a rate 8 times the rate of change of the x-coordinate. The points are (4, 11) and (-4, -31/3).
- Which one of the following statements is incorrect?
⚔️ Practice JEE Main Maths free + battle 1v1 →