The graph above shows a circle centred at the origin, O. The point P lies on the circle and has coordinates (-27, -36). Line QR is a tangent to the circle passing through the point P.Name: Date:

Answer the following questions:

1) Calculate the distance OP

2) Hence write down the equation of the circle

3) Calculate the equation of the tangent line QR

4) The tangent line cuts the y-axis at point R. Calculate the coordinates of point R

5) Calculate the area of triangle OPR to 1 d.p.

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2) The equation of the circle is 𝑥

3) The equation of the tangent line QR is y=-{\Large \frac{3}{4}}x-{\Large \frac{225}{4}}

4) R =(0, -{\Large \frac{225}{4}})

5) 0.5 x 45 x 33.75 ≈ 759.4

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# Answers

1) Using Pythagoras, (OP)^{2}= (-27)

^{2}+ (-36)

^{2}=> OP = 45

2) The equation of the circle is 𝑥

^{2}+ 𝑦

^{2}= 2025

3) The equation of the tangent line QR is y=-{\Large \frac{3}{4}}x-{\Large \frac{225}{4}}

4) R =(0, -{\Large \frac{225}{4}})

5) 0.5 x 45 x 33.75 ≈ 759.4

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