2025 Beatty Sec 3 EOY Q12

2025 Beatty Sec 3 EOY Q12

Secondary 3
8 marks

The equation of a circle \(C_1\) is \((x+1)(4x+3)=(3-y)(4y+1)\).

  1. Express the equation of circle \(C_1\) in its standard form \((x-a)^2+(y-b)^2=r^2\).[2]
  2. Another circle \(C_2\) is formed when \(C_1\) is reflected about the \(x\)-axis. Find the equation of the circle \(C_2\), leaving your answer in general form \(x^2+y^2+2gx+2fy+c=0\).[1]
  3. Hence, find the length of the chord formed when the line \(y=2x\) intersects the circle \(C_1\).[5]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(\left(x+\dfrac78\right)^2+\left(y-\dfrac{11}{8}\right)^2=\dfrac{85}{32}\); (b) \(x^2+y^2+\dfrac74x+\dfrac{11}{4}y=0\); (c) \(1.68\) units.

Need help? Join our JC Math tuition classes.

Learn more