Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2014MathematicsApplication of Derivatives

The point on the circle x²+y²=2 at the abscissa and ordinate increase at the same ate is

Options

  1. A(-1,-1)
  2. B(1,-1)
  3. C(1,1)
  4. D(-1,4)

Correct answer

B. (1,-1)

Step-by-step solution

Given, equation of circle is x²+y²=2 ...(i) Taking derivative w.r.t. ' t ' on both sides. 2 x d x d t +2 y d y d t =0 x d x d t +y d y d t =0 If abscissa and ordinate increase at the same rate, we have d x d t = d y d t x d x d t +y d x d t =0 d x d t (x+y)=0 Since, x+y=0 x=-y ...(ii) Solving Eqs. (i) and (ii), we get x²+(-x)²=2 x= 1 For x=1, y=-1 and x=-1, y=1 Required point are (1,-1) and (-1,1) .

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All COMEDK PYQs