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If the point P(4, -2) is the one end of ...

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

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The correct Answer is:
4
(4) `y^(2)=x`
`:." "4a=1`
`P(at_(1)^(2),2at_(1))-=(4,-2)`
`:." "t_(1)=-4`
Also, `t_(1)t_(2)=-1` as PQ is a focal chord.
Slope of tangent at `t_(2)` is `(1)/(t_(2))=-t_(1)=4`
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CENGAGE-PARABOLA-Exercise (Numerical)
  1. Two tangent are drawn from the point (-2,-1) to parabola y^2=4xdot if ...

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  2. The equation of the line touching both the parabolas y^(2)=4xandx^(2)=...

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  3. If the point P(4, -2) is the one end of the focal chord PQ of the para...

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  4. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

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  5. The locus of the midpoints of the portion of the normal to the parabol...

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  6. Consider the locus of center of the circle which touches the circle x^...

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  7. If on a given base BC[B(0,0) and C(2,0)], a triangle is described such...

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  8. PQ is any focal chord of the parabola y^(2)=8x. Then the length of PQ ...

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  9. The length of focal chord to the parabola y^(2)=12x drawn from the poi...

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  10. From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If ...

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  11. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

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  12. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

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  13. If the circle (x-6)^(2)+y^(2)=r^(2) and the parabola y^(2)=4x have max...

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  14. The slope of line which belongs to family (1+ l) x + (1-l)y + 2(1-l) =...

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  15. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

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  16. Normals at (x(1),y(1)),(x(2),y(2))and(x(3),y(3)) to the parabola y^(2)...

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  17. Foot of perpendicular from point P on the parabola y^(2)=4ax to the ax...

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  18. about to only mathematics

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  19. about to only mathematics

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  20. If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)...

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