Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

Condition that 2 curves y 2 = 4 a x , x y = c 2 cut orthogonally is

Options

  1. Ac 2 = 16 a 2
  2. Bc 2 = 32 a 2
  3. Cc 4 = 16 a 4
  4. Dc 4 = 32 a 4

Correct answer

D. c 4 = 32 a 4

Step-by-step solution

Given y 2 = 4 a x ,   x y = c 2 For y 2 = 4 a x , 2 y d y d x = 4 a i.e. d y d x x 1 , y 1 = 2 a y 1 For x y = c 2 , x d y d x + y = 0 i.e. d y d x x 1 , y 1 = - y 1 x 1 For orthogonal intersection of both curves 2 a y 1 × - y 1 x 1 = - 1 i.e. x 1 = 2 a Also, y 1 2 = 4 a x 1 ⇒ y 1 2 = 8 a 2 and x 1 y 1 2 = c 2 2 ⇒ c 4 = 4 a 2 × 8 a 2 = 32 a 4

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 AP EAMCET PYQs