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  • The area of the triangle formed by joining the origin to the points of intersection of the line <img alt="\sqrt{5} \mathrm{x}+2 \mathrm{y}=3 \sqrt{5}" src="https://entrancecorner.oncodecogs.co

The area of the triangle formed by joining the origin to the points of intersection of the line \sqrt{5} \mathrm{x}+2 \mathrm{y}=3 \sqrt{5}  and circle \mathrm{x}^2+\mathrm{y}^2=10  is
 

Option: 1

6


Option: 2

5


Option: 3

4


Option: 4

3


Answers (1)

best_answer

The equation of lines joining origin and point of intersection of \mathrm{\sqrt{5 x}+2 y=3 \sqrt{5}}  and \mathrm{\mathrm{x}^2+\mathrm{y}^2=10}, is

\mathrm{x^2+y^2=10\left(\frac{\sqrt{5 x}+2 y}{3 \sqrt{5}}\right)^2 \text { or } x^2-y^2+8 \sqrt{5 x y}=0 }

\Rightarrow These lines are perpendicular
\Rightarrow Area of triangle = \frac{1}{2} \times \text{base} \times \text{height} =\frac{1}{2} \times \text{radius} \times \text{radius} =\frac{1}{2} \times \sqrt{10} \times \sqrt{10}=5

Posted by

Irshad Anwar

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