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  • If the length of the chord of the circle  along the line <img alt="y - 2x = 3" src="h

If the length of the chord of the circle x^2 + y^2 = r^2 \ (r>0) along the line y - 2x = 3 is r then r^{2} is equal to 
Option: 1 \frac{9}{5}
Option: 2 12
Option: 3 \frac{12}{5}
Option: 4 \frac{24}{5}

Answers (1)

best_answer

Length of the chord by the line y = mx + c on the circlex^2+y^2=a^2 is

=2\sqrt{\frac{a^2(1+m^2)-c^2}{1+m^2}}

Given equation of line, y = 2x +3

and circle x^2 + y^2 = r^2

according to question

\\r=2\sqrt{\frac{r^2(1+4)-9}{1+4}}\\\frac{r^2}{4}=\frac{5r^2-9}{5}\\r^2=\frac{12}{5}

 

Posted by

himanshu.meshram

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