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Circles Lecture - 1: Sameer Chincholikar

The document provides information about circles including definitions, equations, and examples. It defines a circle as the locus of points at a constant distance from a fixed point. It gives the standard forms of the equation of a circle including the center-radius form (x-h)2 + (y-k)2 = r2 and the general form x2 + y2 + 2gx + 2fy + c = 0. It also provides example problems finding equations of circles given conditions like three points or tangency with another circle.

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Prathamesh Nawale
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127 views33 pages

Circles Lecture - 1: Sameer Chincholikar

The document provides information about circles including definitions, equations, and examples. It defines a circle as the locus of points at a constant distance from a fixed point. It gives the standard forms of the equation of a circle including the center-radius form (x-h)2 + (y-k)2 = r2 and the general form x2 + y2 + 2gx + 2fy + c = 0. It also provides example problems finding equations of circles given conditions like three points or tangency with another circle.

Uploaded by

Prathamesh Nawale
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Circles

Lecture - 1

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Sameer Chincholikar
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Circles
Circle
It is the locus of a point which moves in a plane in such
Definition a way that its distance from a fixed point is always
constant.
Equation of
Circle
Center Radius Form
1. x2 + y2 = a2, where the centre is (0, 0) and the radius is a.
Center Radius Form
2. (x - h)2 + (y - k)2 = a2, where the centre is (h, k) and the radius is a.
Example The line 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area
154 sq. units. Then the equation of this circle is

A. x2 + y2 + 2x - 2y = 62 B. x2 + y2 + 2x - 2y = 47

C. x2 + y2 - 2x + 2y = 47 D. x2 + y2 + 2x - 2y = 62
General Equation of a Circle
General Equation of a Circle

The general equation of a circle is x2 + y2 + 2gx + 2fy + c = 0, where the


centre is (-g, -f) and the radius is
Example A square is inscribed in the circle x2 + y2 - 2x + 4y + 3 = 0, its sides are
parallel to the coordinates axes. The one vertex of the square is

A. (1 + √2, -2) B. (1 , -2)

C. (1, -2+√2) D. None of these


Example From the point A(0, 3) on the circle x2 + 4x + (y - 3)2 = 0, a chord AB is
drawn and extended to a point M such that AM = 2AB. The equation of
the locus of M is ……...
Example The locus of the centre of a circle of radius 1 unit which rolls on
the outside of the circle x2 + y2 + 3x - 6y - 9 = 0 is

A. x2 + y2 + 3x - 6y + 5 = 0 B. x2 + y2 + 3x - 6y - 19 = 0

C. 4x2 + 4y2 + 12x - 24y + 29 = 0 D. None of these


Equation of a Circle Passing through
three non-collinear points
Example If the points (2, 0), (0, 1), (4, 5) and (0, k) are concyclic, then the
value of k is:

A. 1 B. 14/3

C. 5 D. None of these
Example The centre of a circle passing through the points (0, 0), (1, 0) and
touching the circle x2 + y2 = 9 is

A. B. C. D.
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