The equations of the circle S_1 is x^2 + y^2 + 2x - 8y + 9 = 0 and equation of another circle S_2 is x^2 + y^2 - 4x - 14y + 51 = 0. a. Write down the centre and the radius of S_1. b. State the equation of S_2 in the form (x - h)^2 + (y - k)^2 = r^2. c. Show that the two circles touch each other externally and find the coordinates of the point of the contact. d. Obtain the equation of the common tangent to the circles.
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Find the center and radius of circle S1. The equation of circle S1 is given by: x^2 + y^2 + Zx - 8y + 9 = 0 We can rewrite this equation in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, by completing the square for both x and y terms. (x^2 + Zx) + Show more…
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