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If t1a n dt2 are the ends of a focal cho...

If `t_1a n dt_2` are the ends of a focal chord of the parabola `y^2=4a x ,` then prove that the roots of the equation `t_1x^2+a x+t_2=0` are real.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equations of normal to the parabola y^2=4a x at the ends of t...

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  2. The coordinates of the ends of a focal chord of the parabola y^2=4a x ...

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  3. If t1a n dt2 are the ends of a focal chord of the parabola y^2=4a x , ...

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  4. If the length of focal chord of y^2=4a x is l , then find the angle be...

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  5. If length of focal chord P Q is l , and p is the perpendicular distanc...

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  6. Find the equation of the tangent to the parabola y^2=8x having slope 2...

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  7. Find the equation of tangents of the parabola y^2=12 x , which passes ...

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  8. If the line y=3x+c touches the parabola y^2=12 x at point P , then fin...

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  9. Find the equation of the tangent to the parabola y=x^2-2x+3 at point (...

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  10. Find the equation of the tangent to the parabola x=y^2+3y+2 having slo...

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  11. Find the equation of tangents drawn to the parabola y=x^2-3x+2 from th...

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  12. If a tangent to the parabola y^2=4a x meets the x-axis at T and inters...

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  13. The parabola y^2=4x and the circle having its center at (6, 5) inters...

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  14. The tangents to the parabola y^2=4a x at the vertex V and any point P ...

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

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  16. A tangent to the parabola y^2=8x makes an angle of 45^0 with the strai...

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

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  18. If the lines L1 and L2 are tangents to 4x^2-4x-24 y+49=0 and are norma...

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

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

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