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Show that the equation of the chord of the parabola `y^2=4ax` through the points `(x_1,y_1)` and `(x_2,y_2)` on its `(y-y_1)(y-y_2)=y^2-4ax.

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Show that the equation of the chord of the parabola y^(2) = 4ax through the points (x_(1),y_(1)) and (x_(2),y_(2)) on it is (y-y_(1))(y-y_(2)) = y^(2) - 4ax

Show that the equation of the cord.of the parabola x^2=4ay through (x_1,y_1) and (x_2,y_2) the points on its is (x-x_1)(x-x_2)=x^2-4ay.

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Length of the shortest normal chord of the parabola y^2=4ax is

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

If a straight line pasing through the focus of the parabola y^(2) = 4ax intersects the parabola at the points (x_(1), y_(1)) and (x_(2) , y_(2)) then prove that y_(1)y_(2)+4x_(1)x_(2)=0 .

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

PATHFINDER-PARABOLA, ELLIPSE AND HYPERBOLA-QUESTION BANK
  1. If (at^(2) , 2at) be the coordinate of an extremity of a focal chord o...

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  2. The directrix of a parabola is x + y + 4 = 0 and vertix is the point (...

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  3. Show that the equation of the chord of the parabola y^2=4ax through th...

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  4. The pt. (2+4costheta, 1+2sintheta) represents the parametric coordinat...

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  5. If eccentricities of the ellipse x^2/36+y^2/25=1 and x^2/a^2+y^2/b^2=1...

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  6. The length of the latus rectum of the ellipse 2x^2+4y^2=16 is

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  7. The coordinates of the foci of the ellipse 20x^2+4y^2=5 are

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  8. The length of the semi-major axis of an ellipse is 13 and its eccentri...

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  9. The eccentricy of the ellipse x^2+4y^2+2x-24y+33=0 is

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  10. find the length of the latus rectum of the ellipse (x^(2))/(9) +(y^(...

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  11. The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 ...

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  12. If the distance between the foci of an ellipse is equal to the length ...

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  13. Find the eccentricity, the length of latus rectum and the centre of e...

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  14. Find the eccentricity of the ellipse if the length of minor axis ...

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  15. The eccentricity of an ellipse whose distance between the foci is 4 an...

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  16. Taking major and minor axes as x and y - axes respectively , find the ...

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  17. Find the equation of the ellipse whose foci (0,+-4) and the equation o...

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  18. The eccentricity of an ellipse is (2)/(3) focus is S(5,4) and the ma...

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  19. Find the equation to the ausiliary circle of the ellipse 4x^(2) +9...

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  20. The coordinates of the focus of an ellipse are (1,2) and eccentricity...

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