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y ^(2) = 4 ax is the standard form of p...

`y ^(2) = 4 ax ` is the standard form of parabola when curve lies on X axis.

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Standard form of parabola is x ^(2) = - 4 by, when curve lies in the positive Y axis.

Prove that the chord y-x sqrt(2)+4a sqrt(2)=0 is a normal chord of the parabola y^(2)=4ax . Also find the point on the parabola when the given chord is normal to the parabola.

Knowledge Check

  • A square has one vertex at the vertex of the parabola y^2 = 4ax and the diagonal through the vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the co-ordinates of the vertices of the square are

    A
    `(4a,4a)`
    B
    `(4a-4a)`
    C
    `(0,0)`
    D
    `(8a,0)`

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    Find the ara of the region bounded by : (i) the parabola y = x^(2) and the line y=x (ii) the parabola y ^(2) =x and line x+ y =2 (iii) the curve x ^(2) = 4y and the straight line x = 4y -2 (iv) the parabola y ^(2) = 4 ax and the chord y = mx (v) the parabola y ^(2) = 4 ax and its latus-rectum (vi) the parabola (I) y ^(2) = 8x (II) y ^(2) = 6x and the latus rectum.

    Find the point P on the parabola y^(2)=4ax such that area bounded by the parabola,the x- axis and the tangent at P equal to that of bourmal by the parabola,the x-axis and the normal at P.

    The Locus of the point P when 3 normals drawn from it to parabola y^(2)=4ax are such that two of them makes complementary angles with X axis is

    Find the area bounded by the parabola x =4 -y ^(2) and y -axis.

    Find the area bounded by the parabola x =4 -y ^(2) and y -axis.

    y= -2x+12a is a normal to the parabola y^(2)=4ax at the point whose distance from the directrix of the parabola is

    Find the inclination from X - axis of the tangent at point (a, 2a) of the curve y^(2) = 4ax .

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