Line lx + my + n = 0 is normal to circle {x^2} + {y^2} + 2gx + 2fy + c = 0 , if

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10-1.Circle and System of Circles

easy

The line $lx + my + n = 0$ is normal to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$, if

A

$lg + mf - n = 0$

B

$lg + mf + n = 0$

C

$lg = mf - n = 0$

D

$lg - mf + n = 0$

Solution

(a) Since nomal always passes through centre of circle, therefore $( – g,\; – f)$ must lie on $lx + my + n = 0$.

Hence $lg + mf – n = 0$ .

Standard 11

Mathematics

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