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Circle

Section: Mathematics

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Question : 20 of 89

Marks: +1, -0

If the circle passing through

(3,5),(5,5)

(3,-3)

cuts the circle

x^2+y^2+2x+2fy=0

orthogonally, then

f=

[AP EAPCET 22 May 2025 S1]

$-12$
$-3$
$-15$
$-4$

Solution:

Equation of circle passes through

(3,5),(5,5)

and

(3,-3)

is

Let equation be

x^2+y^2+2gx+2fy+c=0

This is passes through

(3,5),(5,5)

and

(3,-3)

6g+10f+c=-34

10g+10f+c=50

6g-6f+c=-18

From Eqs. (i), (ii) and (iii)

g=-4

,

f=-1 \;\text{ and }\; c=0

Required equation of circle

x^2+y^2-8x-2y=0

and given circle is

x^2+y^2+2x+2fy=0

are orthogonal

2(-4)(1)+2(-1)f\;=0+0

f\;=-4

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