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Square of the area of the triangle formed by end points of a focal chord PQ of length 32 units of the parabola y 2 =8x and its vertex,is

Square of the area of the triangle formed by end points of a focal chord PQ of length 32 units of the parabola y2=8x and its vertex,is

Grade:12

1 Answers

ats
103 Points
3 years ago
The lenght of a focal chord of a parabola of the form y2= 4ax is given by a (t+1/t)2. Using this formula, you can find the value of t which is the parameter of one end of the focal chord. Now, the prameter of the other end of the focal chord will be -1/t. Now you have the end points of the focal chord. The vertex of the parabola is the origin. Since you have the coordinates of the three vertices of the triangle you can find its area using the formula for finding the area of a triangle which is ½ ( x1 (y2-y3) + x2 (y3-y1) +  x3 (y1-y2) ) where xi and yi are the coordinates of the vertices.

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