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Prove that the normals at the points (1...

Prove that the normals at the points (1,2) and (4,4) of the parbola `y^(2)=4x` intersect on the parabola.

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Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

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The angle between the tangents drawn from the point (1, 4) to the parabola y^(2)=4x is -

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Prove that the normal at (am^(2),2am) to the parabola y^(2)=4ax meets the curve again at an angle tan^(-1)((1)/(2)m) .

Prove that the the middle points of the normal chords of the parabola y^(2)=4ax is on the curve (y^(2))/(2a)+(4a^(3))/(y^(2))=x-2a

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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) .

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CHHAYA PUBLICATION-TANGENT AND NORMAL -SHORT ANSWER TYPE QUESTIONS
  1. Find the eqauations of the tangent to the ellipse 4x^(2)+9y^(2)=36 at ...

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  2. Find the equation of the tangent to the parabola y^(2)=8x which is inc...

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  3. Find the equation of the tangent to the ellise x^(2)+16y^(2)=16 at the...

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  4. Find the equation of the tangnet to the hyperbola 3x^(2)-4y^(2)=12, wh...

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  5. Prove the equation of the tangent from any point on the line 3x-8y+2=0...

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  6. If the length of the length drawn from (f,g) to the circle x^(2)+y^(2...

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  7. Show that the equation of the normal to the ellipse (x^(2))/(25)+(y^(2...

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  8. Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-...

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  9. Find the equation of normal to the hyperbola x^(2)-y^(2)=16 " at " (4...

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  10. Find the equation of normal to the parabola y^(2)=4x, paralle to the s...

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  11. Find the equation of normal to the ellipse x^(2)+4y^(2)=4 at (2 ,1).

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  12. Find the equation of that normal to the parabola x^(2)=4ay which maeks...

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  13. Find the eqaution of that normal to the hyperbola 3x^(2)-2y^(2)=10 at ...

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  14. Find the equation of normal to the parabola y^(2)=12x at (3t^(2),6t)....

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  15. Prove that the normals at the points (1,2) and (4,4) of the parbola y...

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  16. Find the equation of the normal to the hyperbola x^(2)=4y drawn at (2,...

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  17. Find the equation of the normal to the hyperbola x^(2)-y^(2)=9 at the...

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  18. Find the equation of the normal to the curve x^(2)=4y, which passes th...

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  19. Find the equation of the normal at the points on the curve y=(x)/(1-x^...

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  20. A tangent is drawn to the curve x^(2)(x-y)+a^(2)(x+y)=0 at the origin....

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