First slide

Equation of line in Straight lines

Question

Two sides of a triangle are $y = m_{1} x$ and $y = m_{2} x$ ; $m_{1}, m_{2}$ are the roots of the equation $x^{2} + a x - 1 = 0$ . For all values of ‘a’, the orthocenter of the triangle lies at

Moderate

A

(1, 1)
B

(2, 2)
C

$(\frac{3}{2}, \frac{3}{2})$
D

(0, 0)

Solution

$y = m_{1} x$    $y = m_{2} x$
                 $x^{2} + a x - 1 = 0$
                 $m_{1} . m_{2} = - 1$
The orthocenter of the right angled triangle is vertex at right angle
since the given triangle is right angled triangle, the point of intersection of perpendicular sides is vertex at right angle,
and it is orthocentre of the triangle
therefore, the orthocenter = (0,0)

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