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  • For a triangle OAB where O is (0, 0), A is (1, –1), and B is (2, –3) the circle <img alt="\mathrm{x^2+y^2+4 x+6 y-5=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5

For a triangle OAB where O is (0, 0), A is (1, –1), and B is (2, –3) the circle \mathrm{x^2+y^2+4 x+6 y-5=0} 0 has orthocentre of \mathrm{\Delta OAB} as

Option: 1

an interior point
 


Option: 2

exterior point
 


Option: 3

a point on the circumference of the circle
 


Option: 4

none of these


Answers (1)

best_answer

Let     \mathrm{S(x, y)=x^2+y^2+4 x+6 y-5} 

Then \mathrm{S(0,0)=-5<0 \Rightarrow O\: is\: inside\: the\: circle

        \mathrm{S(1,-1)=-5<0 \Rightarrow A\; is\; inside\; the\; circle}

 As all the three points O, A, and B lie inside the triangle, the orthocentre of the triangle also lies inside the circle.

Posted by

Ritika Kankaria

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