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Equation of a Chord Joining Two Points with Circle in Parametric Form

If the equati...

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If the equations of two circles whose radii are a, a' are S= 0 and S'=0, then show that the circles S/a + S'/a' =0 and S/a - S'/a' = 0 intersect orthogonally.

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Q. If the equations of the circles whose radii are

r

R

be respectively

S = 0

S^{'} = 0

, then prove that the circles

\frac{S}{r} \pm \frac{S^{'}}{R} = 0

will cut orthogonally.

Q. lf a circle cuts three circles

S = 0, S^{'} = 0

S^{''} = 0

orthogonally, then its equation is

Q. The vertices of a triangle are

A (2, - 1), B (3, 1)

C (1, - 2) .

Three circles are drawn with

A B, B C, C A

as diameters. If a circle

S = 0

intersects all the three circles orthogonally, then the radius of

S = 0

S = 0

passes through points of intersection of circles

x^{2} + y^{2} - 2 x + 4 y - 1 = 0

x^{2} + y^{2} + 4 x - 2 y - 5 = 0

and cuts the circle

x^{2} + y^{2} = 4

orthogonally. Then length of tangent from origin on circle

S = 0

Q. The centre of the circle

S = 0

lie on the line

2 x - 2 y + 9 = 0

S = 0

cuts orthogonally the circle

x^{2} + y^{2} = 4

. Show that circle

S = 0

passes through two fixed points & find their coordinates.

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Equation of a Chord Joining Two Points with Circle in Parametric Form

Standard XII Mathematics

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