Lesson Posted on 18/08/2018 Circles

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

The equation of a circle with its centre at C(x0, y0) and radius r is: (x – x0)2 + (y – y0)2 = r2 If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2. If r = 0 then the circle represents a point or a point... read more

**The equation of a** circle with its centre at C(x_{0}, y_{0}) and radius r is:

(x – x_{0})^{2} + (y – y_{0})^{2} = r^{2}

If x = y_{0} = 0 (i.e. the centre of the circle is at origin) then **equation of the circle **reduce to x^{2} + y^{2} = r^{2}**.**

If r = 0 then the circle represents a point or a point circle.

The equation x^{2} + y^{2} + 2gx + 2fy + c = 0 is the general equation of a circle with centre

(–g, –f) and radius √(g^{2}+f^{2}-c).

Equation of the circle with points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) as extremities of a diameter is

(x – x_{1}) (x – x_{2}) + (y – y_{1})(y – y_{2}) = 0.

For general circle, the equation of the chord is x_{1}x + y_{1}y + g(x_{1} + x) + f(y_{1} +y) + c = 0

For circle x^{2} + y^{2} = a^{2}, the equation of the chord is x_{1}x + y_{1}y = a^{2}

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Comments Answered on 05/12/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

Find the length of the tangent from a point which is at a distance of 5 cm from the centre of the circle of radius 3 cm?

Tanay Likhar

Math Mentor

So, if you draw a circle it will form a right angle triangle with hypotenuse 5 cm and base 3 cm. using Pythagoras theorem, the length will be equal to 4 cm.

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Answers 1 Comments Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What is the distance of AB from the centre of the circle if AD is a diameter of a circle and AB is a... read more

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

If non-parallel sides of a trapezium are equal, prove that it is circle?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What do you mean by tangents of a circle?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What do you mean by Chords of a circle?

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