Find an equation of the circle with centre C(5, -3) that passes through the point A(-2, 1) in the form (x-a)^2 + (y-b)^2 = k

step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k is a constnat representing the radius squared. calculate the radius of the circle using pythaogras. distance from centre to point A in the x direction is 5-(-2)=7. distance from centre to point B in the y direction is 1-(-3)= 4. using pythagoras we know that A^2=B^2 + C^2. this means the radius^2 = X distance^2 + Y distance^2.
so r^2 = 7^2 + 4^2. r^2 = 49+16=65.

Step 3. putting both centre component and radius together we obtain (x-5)^2 + (y+3)^2 = 65. This is the equation of the circle.

TW
Answered by Tim W. Maths tutor

4660 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

integrate cos^2(2x)sin^3(2x) dx


Points P and Q are situated at coordinates (5,2) and (-7,8) respectively. Find a) The coordinates of the midpoint M of the line PQ [2 marks] b) The equation of the normal of the line PQ passing through the midpoint M [3 marks]


Does the equation: x^2+5x-6 have two real roots? If so what are they?


express (3x + 5)/(x^2 + 2x - 15) - 2/(x - 3) as a single fraction its simplest form


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