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  • The image of the circle <img alt="\mathrm{x^2+y^2+16 x-24 y+183=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2&plus;16%20x-24%20y&plus;183%3D

The image of the circle \mathrm{x^2+y^2+16 x-24 y+183=0}  by the line mirror \mathrm{4 x+7 y+13=0}  is
 

Option: 1

\mathrm{ x^2+y^2-32 x-4 y-235=0 }


Option: 2

\mathrm{x}^2+\mathrm{y}^2+4 \mathrm{x}+7 \mathrm{y}+13=0


Option: 3

\mathrm{ x^2+y^2+32 x+4 y+235=0 }


Option: 4

\mathrm{x^2+y^2-32 x+4 y+235=0 }


Answers (1)

best_answer

 The given circle is (-8,12), 5
line is \mathrm{4 x+7 y+13=0} .
The required circle will be (\mathrm{h}, \mathrm{k}), 5  where (\mathrm{h}, \mathrm{k}) is the reflection of centre (-8,12)  in the given
line \frac{\mathrm{h}-\alpha}{\mathrm{a}}=\frac{\mathrm{k}-\beta}{\mathrm{b}}=-\frac{2 l}{\mathrm{a}^2+\mathrm{b}^2}  or \frac{\mathrm{h}+8}{4}=\frac{\mathrm{k}-12}{7}=-2

Circle  \mathrm{x^2+y^2+32 x+4 y+235=0}.

Posted by

Sanket Gandhi

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