Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2010MathematicsApplication of Derivatives

For the curve 4 x⁵=5 y⁴ , the ratio of the cube of the subtangent at a point on the curve the square of the subnormal at the same point is

Options

  1. A4⁴ 5
  2. B5⁴ 4
  3. C4⁴ 5⁴
  4. D( 5 4 )⁴

Correct answer

C. 4⁴ 5⁴

Step-by-step solution

The given curve is 4 x⁵=5 y⁴ gathered 20 x⁴=20 y³ d y d x d y d x = x⁴ y³ gathered We know that Length of subnormal (S N)= (y d x d y )= ( y⁴ x⁴ ) Length of subtangent ( ST )= ( y dy dx )= ( x ⁴ y ² ) But given condition is aligned ( SN )³ ( ST )² = ( y ⁴ / x ⁴ )³ ( x ⁴ / y ² )² = ( y ⁴ x ⁴ )³ ( y ² x ⁴ )² = y ¹² x ¹² y ⁴ x ⁸ = ( y ¹⁶ x ²⁰ ) = ( y ⁴ x ⁵ )⁴ = ( 4 5 )⁴= 4⁴ 5⁴ ( 4 x ⁵=5 y ⁴ ) aligned

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 KCET PYQs