Aiming the Communication Device You reach the communication device and are alerted by your computer that the communication device is 2 surrounded by a force field that can be described by the equation, x² + y² = (¹ x² + ¹ y² − y)², with - 4 the origin being where you located this device. The inhabitants of this planet did not want unwelcomed guests, so they made sure to guard the use of this device. Your computer helpfully generates a plot of this equation and tells you that it is a cardioid (whatever that means). The communication device can be taken to the very edge of the force field, but not beyond it. In fact, the only way to use the device is to align it tangent to the force field. Your computer also recovers some files that give points along the force field where the communication device can be used to communicate with different planets. Communication with your home planet can be achieved from the point on the force field, (-4,0). If you provide your computer with the equation of the line that satisfies these conditions, you will be able to send a message to your home world. What equation do you provide your computer? -2 y 7- 6- 5- 4- 3- 2 T 1- -2

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