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# If normal at point P on parabola y^{2} = 4ax, (a > 0) meet it again at Q is such a way that OQ is of minimum length where O is vertex of parabola, then ΔOPQ is

- a right angled triangle
- obtuse angled triangle
- acute angled triangle
- None

## The correct answer is: a right angled triangle

### Normal at P(t_{1}) meets at Q(t_{2})

t_{2} =

For minimum length of OQ, |t_{2}| should be minimum

i.e. | t_{2} | =

If t_{2} = t_{1} =

Slope of OQ = = m_{1} and of OQ = = m_{2}

m_{1}m_{2} = –1 OPQ is right angled triangle.

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