A pendulum bob and string with tangential direction is modelled by the equation $2y + 4x = -20$. A

Question

A pendulum bob and string with tangential direction is modelled by the equation $2y + 4x = -20$.

A physicist spilled coffee on his notes and the equation for the curved path of the pendulum bob became $x^2 + y^2 + ax - 2y + 5 = 0$, where $a$ is now an unknown constant.

Find the possible lengths of the pendulum string in centimetres.

Accepted Answer

When $a = -94, \text{Length} \approx 47.0$ cm (to $3$ s.f.); When $a=6, \text{Length} \approx 2.24$ cm (to $3$ s.f.)

Coordinate Geometry - Finding the Centre and Radius of a Circle

Coordinate Geometry - Finding the Centre and Radius of a Circle

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