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If the point P(4,-2) is one end of the focal chord PQ of parabola y^2=x then the slope of the tangent at Q is?

If the point P(4,-2) is one end of the focal chord PQ of parabola y^2=x then the slope of the tangent at Q is?

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1 Answers

Arun
25763 Points
2 years ago
the parabola is of the form y^2=4ax, 
So, here, a=1/4, 
So, focus is S(1/4,0), 
Since PQ is focal chord, it passes thru P(4,-2) and focus S(1/4,0), 
Find its equation! i.e PS which bcomes equation of PQ, 
It comes out to be, 15y 8x=2,! 
Now solve this equation wid parabola, y^2=x, you get 2 pts, 1 is P and other is Q which comes out as (1/64,1/8), 
Now, find dy/dx, i.e differentiate the parabola at y=1/8! 
This the slope of the tangent at Q=4

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