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Find the value of alpha for which the po...

Find the value of `alpha` for which the point `(alpha -1, alpha)` lies inside the parabola `y^(2) = 4x`.

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To find the value of \( \alpha \) for which the point \( (\alpha - 1, \alpha) \) lies inside the parabola defined by the equation \( y^2 = 4x \), we can follow these steps: ### Step 1: Identify the condition for the point to be inside the parabola The parabola \( y^2 = 4x \) opens to the right. A point \( (x, y) \) lies inside the parabola if the following condition holds: \[ y^2 < 4x \] ...
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MOTION-PARABOLA-EXERCISE - IV
  1. Find the value of alpha for which the point (alpha -1, alpha) lies ins...

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  2. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

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  3. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

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  4. A parabola has the origin as its focus and the line x""=""2 as the ...

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  5. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  6. Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . ...

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  7. The equation to the line touching both the parabolas y^2 =4x and x^2=...

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  8. Let O be the vertex and Q be any point on the parabola,x^2=""8y . I...

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  9. Let , P be the point on the parabola y^(2) = 8x which is at a min...

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  10. The centres of those circles which touch the circle x^(2) + y^(2) - 8...

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  11. IF the tangent at (1,7) to the curve x ^(2) = y-6 touches the circle ...

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  12. Tangent and normal are drawn at P(16,16) on the parabola y^2=16x which...

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  13. The axis of a parabola is along the line y=x and the distance of its v...

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  14. The equations of the common tangents to the parabola y = x^2 and y=-...

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  15. Match the following. Normals are drawn at points P Q and R lying on th...

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  16. Statement-1: The curve y=(-x^(2))/2+x+1 s symmetric with respect to th...

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  17. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  18. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  19. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  20. The tangent and normal at P(t), for all real positive t, to the parabo...

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  21. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

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