Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x^2 + y^2= 20

rearrange line equation: x=10 + 2ysubstitute into circle equation: (10+2y)2 + y2=20expand: 4y2 +20y +20y + 100 + y2= 20 collect terms: 5y2 + 40y +100 = 20move all to one side: 5y2 + 40y + 80=0divide by 5: y2 + 8y + 16=0factorise: can use quadratic equation but this one is easy to spot:(y+4)2 =0therefore they meet at y= -4x= 10 + 2(-4) =2line meets the circle at (2, -4)as there is only one point of intersection, it is therefore a tangent

AB
Answered by Annabel B. Maths tutor

10445 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How to find the exact formula of the function if the graph of it is given?


Find values for x and y from two simultaneous equations: 2x + y = 5 and 3x + y = 7


For the equation 7x+3y=10x/y make x the subject.


A bag contains beads, 60% of which are green. A student claims that the probability of getting two green beads if the beads aren't replaced is 1/3 as 6/10 * 5/9 is 1/3. Is the student right?


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