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Since the equation of the circle is x^2+y^2+2gx+2fy+c Show that x2 +y2 =a2 represent the standard equation of a circle whose centre at (0,0) and radius is a The equation of the circle concentric with the circle x2 +y2 +8x+10y−7 =0 and passing through the centre of the circle x2 +y2 −4x−6y =0 is

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Consider the circle x2 +y2 −4x−2y+c = 0 whose centre is a(2,1) Question find all the common tangents to the circles x2 +y2 −2x−6y+9 =0 and x2 +y2 +6x−2y+1 =0 If the point p (10,7) is such that the line segment pa meets the circle in q with p q =5, then c =

Equation of a circle centered at origin with radius r

X2 +y2 = r2 3 Equation of a circle whose center is (h, k) and radius is r (x − h)2 +(y − k)2 = r2 4 Equation of a circle for which the line segment joining two given points is a diameter

Let a (x₁, y₁) and b (x₂, y₂) be two given points. To find the combined equation for the pair of tangents drawn from the origin to the circle with the equation x2 + y2 + 4x + 6y + 9 = 0, you can use the following steps: Figure shown line l = 0 which is radieal axis of s1 =0 and s2 =0 The direct common tangent touches circle s1 = 0 and s2 = 0 at a and b respectively and cuts l= 0 at p.

Find the coordinates of the centres and the radii of the circles whose equation is