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If `y_1, y_2, y_3` be the ordinates of a vertices of the triangle inscribed in a parabola `y^3=4a x ,` then show that the area of the triangle is `1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot`

A

`1/(2a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|`

B

`1/(4a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|`

C

`1/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|`

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Exercise
  1. An equilateral triangle is inscribed in the parabola y^2=4a x whose...

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  2. The coordinates of the focus of the parabola x^(2)-4x-8y-4=0

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  3. If y1, y2, y3 be the ordinates of a vertices of the triangle inscri...

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  4. The area of the triangle inscribed in the parabola y^(2)=4x the ordina...

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  5. The length of the latusrectum of the parbola whose focus is (3, 3) and...

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  6. The length of the latus rectum of the parabola whose focus is ((u^2)/(...

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  7. PQ is a double ordinate of a parabola y^2=4a xdot Find the locus of it...

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  8. If the segment intercepted by the parabola y=4a x with the line l x+m ...

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  9. The length of a focal chord of the parabola y^2=4ax making an angle th...

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  10. Show that the parametric point (2+t^(2),2t+1) represents a parabola. S...

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  11. The ratio in which the line segment joining the point (4, -6) and (3, ...

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  12. If (a , b) is the midpoint of a chord passing through the vertex of th...

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  13. If the vertex and focus of a parabola are (3,3) and (-3,3) respectivel...

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  14. about to only mathematics

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  15. If y(1),y(2) are the ordinates of two points P and Q on the parabola ...

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  16. If the line x + y = 1 touches the parabola y^2-y + x = 0, then the coo...

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  17. Find the locus of the foot of the perpendiculars drawn from the vertex...

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  18. Equation of line touching both the parabolas y^2=4x & x^2=-32y

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  19. If t is the parameter for one end of a focal chord of the parabola y^2...

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  20. Find the equation of normal to the parabola y^2=4axat point (at^2, 2at...

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