A circle has equation x^{2}-8x+y^{2}-6y=d. A line is tangent to this circle and passes through points A and B, (0,17) and (17,0) respectively. Find the radius of the circle.

Gradient of line: (0-17)/(17-0)= -1 equation of line: y-y1=m(x-x1) y-17=-1(x-0) y=17-x equation of circle: (x-4)2+(y-3)2-25=d (completing the square) (x-4)2+(y-3)2=d+25 Substitute equation of line into equation of circle:(x-4)2+(17-x-3)2=d+25, 2x2-36x+(187-d)=0 As the line is tangential to the circle, we want there to be one solution of x to this quadratic, and hence need discriminant to equal 0, (-36)2-(4)(2)(187-d)=0 8d=200 d=25=> (x-4)2+(y-3)2=50 and equation of circle is of form (x-a)2+(y-b)2=r2Thus, r2= 50 and radius of circle is square root 50

AH
Answered by Amirali H. Further Mathematics tutor

2186 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Factorise the following quadratic x^2 - 8 + 16


l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.


Can you explain rationalising surds?


A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences