CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The length of the common chord of the two circles
$$ x^2+y^2-4y=0$$ and $$x^2+y^2-8x-4y+11=0$$ is


A
1454
loader
B
112
loader
C
135
loader
D
1354
loader

Solution

The correct option is D $$\dfrac{\sqrt{135}}{4}$$

$$s_1=x^2+y^2-4y=0$$
$$s_2=x^2+y^2-8x-4y+11=0$$
Equation common chord $$=s_1-s_2=8x-11$$
$$OC= \left|\dfrac{-11}{\sqrt{8^2}}\right|=\dfrac{11}{8}$$
$$CD=\left|\dfrac{32-11}{\sqrt{8^2}}\right|=\left|\dfrac{21}{8}\right|$$
$$AC^2=OA^2-OC^2$$
$$=2^2-\left(\dfrac{11}{8}\right)^2$$
$$=\dfrac{256-121}{64}$$
$$=\dfrac{135}{64}$$
$$AC=\sqrt{\dfrac{135}{64}}=\sqrt{\dfrac{135}{8}}$$
$$2AC=\dfrac{\sqrt{135}}{4}$$ is the length of common chord.

511552_474378_ans.png

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image