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1)The angle between tangents to the parabola y 2 =4ax at the points where it intersects the line x-y-a=0 is ? 2)The length of a focal chord of the parabola y 2 =4ax making an angle ∂ with the axis of the parabola is ?

1)The angle between tangents to the parabola y2=4ax at the points where it intersects
the line x-y-a=0 is ?
2)The length of a focal chord of the parabola y2=4ax making an angle ∂ with the axis of the parabola is ?

Grade:11

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
Hint:
1. (i) Solve the two equations and get the intersecting points.
(ii) Then apply the point form of tangent equation to get the equations of two tangents. (iii) Then find the solve of the two lines and then finally use the following formula
tan(theta) = modulas (m1-m2 / 1 +m1m2) To get the angle between the tangents.

2. From the given equation of parabola, you can easly get the coordinates of focus. Using focus point and angle of focal chord you can get the equation of it and solve these with equation of parabola to get the intersecting points. Then finally apply the distance formula to find its length. \

Thanks.

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