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  • The image of the circle <img alt="\mathrm{x^2+y^2+16 x-24

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

 

Option: 1

\mathrm{x2 + y2 -32x - 4y -235 = 0}


Option: 2

\mathrm{x2 + y2 + 4x + 7y + 13 = 0}


Option: 3

\mathrm{x2 + y2 + 32x + 4y + 235 = 0}


Option: 4

\mathrm{x2 + y2 -32x + 4y + 235 = 0}


Answers (1)

best_answer

The given circle is (−8, 12), 5

line is 4x + 7y + 13 = 0.

The required circle will be (h, k), 5 where (h, 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^{\prime}}{\mathrm{a}^2+\mathrm{b}^2} \text { or } \frac{\mathrm{h}+8}{4}=\frac{\mathrm{k}-12}{7}=-2

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

  

 

 

 

 

Posted by

Rakesh

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