# John decides to use co-ordinate geometry to check his calculations. By studying maps he concludes that the

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## Question:

John decides to use co-ordinate geometry to check his calculations. By studying maps he concludes that the restricted airspace can be presented using a circle with equation: x² + y² - 18x - 14y + 117 = 0.

(a) If John sends his drone on a linear path 2x - 5y + 28 = 0, he will enter into the restricted airspace? Explain your answer.

John places himself at the point (1,6). He plans to send his drone on two paths tangential to the restricted area, of slope m to the airspace.

(b) Show the equation of the paths in terms of m can be expressed as mx - y + (6 - m) = 0.

(c) Find the equations of the two paths of the drone in the form ax + by + c = 0.

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