Question

# If the line segment intercepted by the parabola $${ y }^{ 2 }=4\alpha x$$ on the line $$ax+by+c=0$$ subtends a right angle at the vertex, then

A
4aα+c=0
B
4bα+c=0
C
4aα+b=0
D
none of these

Solution

## The correct option is B $$4a\alpha +c=0$$Making the equation of parabola $${ y }^{ 2 }=4\alpha x$$ homogeneous using the equation of line $$ax+by+c=0$$, we get$$\displaystyle { y }^{ 2 }=4\alpha x\left( \frac { ax+by }{ -c } \right) \Rightarrow 4a\alpha { x }^{ 2 }+4b\alpha xy+c{ y }^{ 2 }=0$$which represents the combined equation of $$OP$$ and $$OQ$$.Since $$\angle POQ={ 90 }^{ 0 }$$, coefficients of $${ x }^{ 2 }+$$ coefficients of $${ y }^{ 2 }=0$$$$\Rightarrow 4a\alpha +c=0$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More