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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)
  1. x22Ax+2A=0
  2. x2Ax+2A=0
  3. x2+2Ax+2A=0
  4. x2+Ax+2A=0


Solution

The correct option is B x2Ax+2A=0
Let 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
x2Ax+2A=0

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