The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.

We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5)
For the second part of the question we must find the gradient of the tangent at point B, so M = dy/dx at (4,2). Thus M = -2/9. We then find the gradient of the normal which is the negative inverse of M = 9/2. Then we use the equation y-2 = 9/2 *(x-4) but let y=0 since we are finding the x-coordinate of A. Doing this, x must equal 32/9 in order for the equation to be satisfied.

Answered by Jake M. Maths tutor

3011 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A radio sells for £63, after a 40% increase in the cost price. Find the cost price.


How many people in a room is required such that the probability of any two people sharing a birthday is over 50 percent?


What is the point of a derivative?


Consider the function y = x.sin(x); differentiate the function with respect to x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences