Question 19
The sketch shows circle C C\,C with centre P(7.5,10)P(7.5, 10)P(7.5,10). The line l l\,l with equation y=12x\displaystyle y = \frac{1}{2}xy=21x is a tangent to C C\,C at point QQQ. The equation of C C\,C is (x−7.5)2+(y−10)2=31.25(x - 7.5)^2 + (y - 10)^2 = 31.25(x−7.5)2+(y−10)2=31.25.
a.[4]
Find the coordinates of QQQ.
b.[4]
The line with equation y=12x+k\displaystyle y = \frac{1}{2}x + ky=21x+k, where k k\,k is a non-zero constant, is also a tangent to CCC. Find the value of kkk.
Circles Questions
292 exam-style questions on Edexcel A Level Maths Circles, covering 6.1 Midpoints and Perpendicular Bisectors, 6.2 Equation of a Circle, 6.3 Intersections of Straight Lines and Circles, 6.4 Use Tangent and Chord Properties, and 6.5 Circles and Triangles. Each one has a worked solution and a mark scheme showing where the marks go.