Analytical Geometry
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?
1 Answer
Arun
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
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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