Question

# A line passes through (2,2) and has x-intercept and y-intercept as α units and β units respectively. It makes a triangle of area A with co-ordinate axes. Then the quadratic equation whose roots are α and β is : (α>0,β>0)x2−2Ax+2A=0x2−Ax+2A=0x2+2Ax+2A=0x2+Ax+2A=0

Solution

## The correct option is B x2−Ax+2A=0Let the equation of line be xα+yβ=1 it passes through (2,2) so 2α+2β=1 ⇒2(α+β)=αβ Here, α and β are intercepts So the area of triangle =12αβ=A ⇒αβ=2A ⇒ α+β=A So, Quadratic equation will be x2−(α+β) x+αβ=0 ⇒x2−Ax+2A=0

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