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  • is a given circle and <img alt="\mathrm{\left(x_1, y_1\right)}" src=

\mathrm{x^2+y^2=16} is a given circle and \mathrm{\left(x_1, y_1\right)} is a point such that \mathrm{x_1{ }^2+y_1{ }^2<15}. The straight line \mathrm{ xx_1+y y_1=16} cuts the circle
 

Option: 1

at two points

 


Option: 2

at one point
 


Option: 3

at no points
 


Option: 4

at two coincident points.


Answers (1)

best_answer

The perpendicular distance from the centre of the circle to the line \mathrm{\mathrm{xx}_1+\mathrm{yy}_1=16} is

\mathrm{ \frac{16}{\sqrt{x_1^2+y_1^2}}>4\left(\text { as } x_1^2+y_1^2<15\right) }

So the line does not cut the circle in any real point.

Hence option 3 is correct.

Posted by

shivangi.shekhar

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