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Show that xcosalpha+ysinalpha=p touches ...

Show that `xcosalpha+ysinalpha=p` touches the parabola `y^2=4a x` if `pcosalpha+asin^2alpha=0` and that the point of contact is `(atan^2alpha,-2atanalpha)dot`

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The parabola y^2=4x and the circle having its center at (6, 5) interse...

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  2. The tangents to the parabola y^(2)=4ax at the vertex V and any point P...

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  3. Show that xcosalpha+ysinalpha=p touches the parabola y^2=4a x if pcosa...

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  4. A tangent to the parabola y^(2)=8x makes an angle of 45^(@) with the s...

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  5. Find the equation of the common tangent of y^2=4a x and x^2=4a y.

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  6. If the lines L(1)andL(2) are tangents to 4x^(2)-4x-24y+49=0 and are no...

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  7. Find the shortest distance between the line y=x-2 and the parabola y=x...

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  8. If two tangents drawn from the point (alpha,beta) to the parabola y^(2...

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  9. Find dy/dx , tan^(-1){(cosx - sinx)/(cosx + sinx)} .

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  10. Find the angle at which normal at point P(at^(2),2at) to the parabola ...

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  11. If tangents are drawn to y^(2)=4aax from any point P on the parabola y...

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  12. Find the equation of a parabola having its focus at S(2,0) and one ext...

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  13. Find the equation of parabola having focus at (0,-3) its directrix ...

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  14. Find the equation of parabola (i) having its vertex at A(1,0) and fo...

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  15. A beam is supported at its ends by supports which are 12 metres apa...

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  16. Find the coordinates of points on the parabola y^2=8x whose focal dist...

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  17. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find t...

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  18. An arch is in the from of a parabola with its axis vertical. The arch ...

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  19. If the vertex of a parabola is the point (-3,0) and the directrix is t...

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  20. The chord A B of the parabola y^2=4a x cuts the axis of the parabola a...

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