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2. Find the centre and radius of the circle with the given equation
(a) x2 + y2 +12x - 10y = 0
(b) 5x2 + 5y2 + 14x + 12y - 10 = 0
(c) x2 + y2 - 6x + 4y + 13 = 0
(d) 4x2 + 4y2 - 8x +12y - 25 = 0
3. Write an equation of the circle that passes through the given points
(a) A(4, 5), B(-4, -3 ), C(8, -3)
(b) A(-7, 7), B(5, -1), C(10, 0)
(c) A(a, 0), B(0, b), C(0, 0)
(d) A(5, 6), B(-3, 2), C(3, -4)
4. In each of the following, find an equation of the circle passing through
(a) A(3, -1), B(0, 1) and having centre at 4x - 3y - 3 = 0
(b) A(-3, 1) with radius 2 and centre at 2x - 3y + 3 = 0
(c) A(5,1) and tangent to the line 2x - y - 10 = 0 at B(3, -4)
(d) A(1, 4), B(-1, 8) and tangent to the line x + 3y - 3 = 0
5. Find an equation of a circle of radius a and lying in the second quadrant such that it
is tangent to both the axes.
6. Show that the lines 3x - 2y = 0 and 2x + 3y - 13 = 0 are tangents to the circle
x2 + y2 + 6x - 4y = 0
7. Show that the circles
x2 + y2 + 2x - 2y - 7 = 0 and x2 + y2 - 6x + 4y + 9 = 0 touch externally.
8. Show that the circles
x2 + y2 + 2x - 8 = 0 and x2 + y2 - 6x + 6y - 46 = 0 touch internally.
9. Find equations of the circles of radius 2 and tangent to the line
x - y - 4 = 0 at A(1, -3).

6.2 TANGENTS AND NORMALS

A tangent to a curve is a line that touches the curve without cutting through it.
dy We know that for any curve whose equation is given by y = f(x) or f(x, y) = 0, the derivative
dx is slope of the tangent at any point P(x, y) to the curve. The equation of the tangent to
the curve can easily be written by the pointslope formula. The normal to the curve at P is
the line through P perpendicular to the tangent to the curve at P. This method can be very

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