Find and simplify the point(s) of intersection of the curves: x^2 + y^2 =6 , y = x - 3

Substituting y = x-3 into the first equation and expanding brackets:(x-3)2+x2 = 6 <=> 2x2 -6x +9 =6 <=> 2x2 -6x +3 =0Solving by using the quadratic formula:x=(6+- sqrt(36-4(2)(3)))/4 = (6+- sqrt(12))/4 Using the product rule for surds:x=(6+- 2sqrt(3))/4 = (3+- sqrt(3))/2Substituting back into y=x-3:y=(-3+- sqrt(3))/2So our final answer is: ( (3+sqrt(3))/2 , (-3+ sqrt(3))/2) and ( (3-sqrt(3))/2 , (-3- sqrt(3))/2)

ER
Answered by Evans R. Maths tutor

2815 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the equation 3x^2 +17x -6 = 0 without using a calculator


Suppose we have a circle with the equation x^2 +y^2 =25. What is the equation to the tangent to the circle at point (4,3)?


How do I find out where two functions meet on a graph?


Solve the simultaneous equations: 6x + 2y = -3, 4x - 3y = 11


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning