Home
Class 12
MATHS
In the curve x^a y^b=K^(a+b) , prove tha...

In the curve `x^a y^b=K^(a+b)` , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 5.2|6 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 5.3|4 Videos

  • 3D COORDINATION SYSTEM

    CENGAGE ENGLISH|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE ENGLISH|Exercise All Questions|142 Videos

Similar Questions

Explore conceptually related problems

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is

Prove that the segment of tangent to xy=c^(2) intercepted between the axes is bisected at the point at contact .

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

If the intercept of a line between the coordinate axes is divided by the point (-5,4) in the ratio 1:2, then find the equation of the line.

If the intercept of a line between the coordinate axes is divided by the point (-5,4) in the ratio 1:2, then find the equation of the line.

Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola y^(2)= 4ax subtends a right angle at its focus.

In the curve x= a (cos t+ log tan(t/2)) , y =a sin t . Show that the portion of the tangent between the point of contact and the x-axis is of constant length.

In the curve x= a (cos t+ log tan(t/2)) , y =a sin t . Show that the portion of the tangent between the point of contact and the x-axis is of constant length.