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  • The triangle formed by the tangents to a parabola  at the ends of the lat

The triangle formed by the tangents to a parabola \mathrm{y^2=4 a x} at the ends of the latus rectum and the double ordinate through the focus is
 

Option: 1

 equilateral
 


Option: 2

 isosceles
 


Option: 3

 right-angled isosceles


Option: 4

 dependent on the value of a for its classification


Answers (1)

The tangents to the parabola \mathrm{y^2=4 a x}  at the points\mathrm{ (a, 2 a),(a,-2 a)} are \mathrm{ y=x+a} and \mathrm{ y=-x-a}.
The third side of the triangle is \mathrm{ x=a}.
Clearly, these lines form a right-angled triangle whose two sides are equal.

Posted by

Sumit Saini

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