Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202120 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

If y = 4 x - 6 is a tangent to the curve y 2 = a x 4 + b at ( 3 , 6 ) , then the values of a & b are

Options

  1. Aa = 4 9    &    b = - 4 9
  2. Ba = 0    &    b = 4 9
  3. Ca = - 4 9    &    b = - 4 9
  4. Da = 4 9    &    b = 0

Correct answer

D. a = 4 9    &    b = 0

Step-by-step solution

y 2 = a x 4 + b ⇒ 2 y d y d x = 4 a x 3 ⇒ d y d x = 4 a x 3 2 y Slope of tangent at 3 , 6 = 4 a × 27 12 = 9 a Given equation of tangent y = 4 x - 6 Slope of tangent = 4 ⇒ 9 a = 4 ⇒ a = 4 9 3 , 6   lies on   y 2 = a x 4 + b ⇒ 36 = 4 9 × 81 + b ⇒ b = 0 Hence, a = 4 9    &    b = 0

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