I'm having a huge amount of trouble with Exercise 3A, questions 10, 11 and 12 from the Heinemann P3 book. As I've got the C2 exam on Monday, any help would be really appreciated. The questions are:
10) Show that the line with equation 2x - 3y + 26 = 0 is a tangent to the circle with equation x² + y² - 4x + 6y - 104 = 0. If T is the point of contact of the tangent with the circle, find the equation of the normal to the circle at T. Find also the coordinates of the point on the circle which is diametrically opposite to T. Answer: 3x + 2y=0; (8, - 12)
11) The line with equation y=mx is a tangent to the circle with equation x² + y² - 6x - 6y + 17 = 0. Find the possible values for m. Answer: (9±√17)/8
12) Prove that the circle with equation x² + y² - 2ax - 2ay + b² = 0 touches the y-axis.
Hence, or otherwise, find equations of the two circles which pass through the points (1,2) and (2,3) and which touch the y-axis. Find the distance between their centers. Answer: x² + y² - 10x + 2y + 1 = 0, x² + y² - 2x - 6y + 9 = 0; 4√2
Thank you so much for taking the time to help me!