Home
Class 12
MATHS
Prove that the curve y = x^2 and xy = k ...

Prove that the curve `y = x^2` and `xy = k` intersect orthogonally if `8k^2 = 1`.

Text Solution

AI Generated Solution

To prove that the curves \( y = x^2 \) and \( xy = k \) intersect orthogonally when \( 8k^2 = 1 \), we will follow these steps: ### Step 1: Find the slopes of the curves The first curve is \( y = x^2 \). To find the slope of this curve, we differentiate it with respect to \( x \): \[ \frac{dy}{dx} = 2x \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise Long answer types questions|10 Videos

  • APPLICATION OF DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPES QUESTIONS|25 Videos

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|22 Videos

Similar Questions

Explore conceptually related problems

Prove that the curves y=x^(3) and xy=k cut each other orthogonally, if 3k= 1.

Prove that the curves "x"="y"^2 and "x y"="k" intersect at right angles if 8"k"^2=1.

Show the condition that the curves a x^2+b y^2=1 and Ax^2+By^2=1 should intersect orthogonally is 1/a-1/b=1/A-1/Bdot

If curve y = 1 - ax^2 and y = x^2 intersect orthogonally then the value of a is

Find the condition that curves 2x=y^(2) and 2xy=k intersect orthogonally.

Show that x^2+4y^2=8 and x^2-2y^2=4 intersect orthogonally

Show that x^2=y and x^3+6y=7 intersect orthogonally at (1,\ 1)

Prove that the curves x^(2)-y^(2)=16 and xy = 15 intersect each other at 90^(@) angle.

Show that x^2=4y and 4y+x^2=8 intersect orthogonally at (2,\ 1)

If the curves y=2\ e^x and y=a e^(-x) intersect orthogonally, then a= (a)1//2 (b) -1//2 (c) 2 (d) 2e^2

Home
Profile