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please answer fast.......if the tangent to the parabola y^2= 4ax at (x1,y1) and (x2,y2) meet on the axis then????? answer is x1=x2 please give solution.............

please answer fast.......if the tangent to the parabola y^2= 4ax at (x1,y1) and (x2,y2) meet on the axis then?????
answer is x1=x2
please give solution.............

Grade:12

1 Answers

Rajat
213 Points
2 years ago
Differentiating the equation of the parabola we get
2y(dy/dx)= 4a
dy/dx = 2a/y
Equation of tangent at(x1,y1) :
y=(2a/y1)x+c
c= y1-(2a/y1)x1
So, equation is y = (2a/y1)x+y1-(2a/y1)x1
Similarly the eqn of tangent at (x2,y2)
y = (2a/y2)x+y2-(2a/y2)x2
Let the tangents meet at ( a,0)
So, (2a^2/y1)+y1=2ax1/y1
And (2a^2/y2)+y2= 2ax2/y2
Now y1^2= 4ax1 and y2^2= 4ax2
So, (2a^2/y1)+y1=(2a/y1)(y1^2/4a)=y1/2
Therefore, 2a^2/y1=(-y1/a)
So, 4a^2= y1^2
Similarly 4a^2= y2^2
So, y1=±y2
Therefore, x1=x2

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