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Find the equations of the chords of the parabola y2 = 4ax which pass through the point (ā6a, 0) and which subtends an angle of 45° at the vertex. Find the equations of the chords of the parabola y2 = 4ax which pass through the point (ā6a, 0) and which subtends an angle of 45Ā° at the vertex.
The vertex of parabola š¦^2=4šš„is (0,0).Equation of a chord in the slope-intercept form isy=kx+b (1)Here k=tan 45Ā°=1, because a chord subtends an angle of 45Ā° at the vertex.So, in fact (1) is given byy=x+b (2)On the other hand, this line passes through the point (ā6a, 0), consequently its coordinates satisfy equation (2):0=-6a+b,b=6a.Finally, y=x+6a is the equation of chord.Answer: y=x+6a.
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