In the parabola `y^2=4a x ,` the length of the chord pasing through the vertex and inclined to the axis at `pi//4` is a.`4sqrt(2)a` b. `2sqrt(2)a` c. `sqrt(2)a` d. none of these

In the parabola y^(2) = 4ax , the length of the chord passing through the vertex and inclined to the x-axis at (pi)/(4) is

Write the length of the chord of the parabola y^2=4a x which passes through the vertex and in inclined to the axis at pi/4 .

If(a, b) is midpoint of a chord passing through the vertex of the parabola y^(2)=4x then

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

The length of the chord of the parabola y^(2) = 12x passing through the vertex and making an angle of 60^(@) with the axis of x is

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

The area of the triangle formed by the tangent and the normal to the parabola y^2=4a x , both drawn at the same end of the latus rectum, and the axis of the parabola is (a) 2sqrt(2)a^2 (b) 2a^2 4a^2 (d) none of these

The area of the triangle formed by the tangent and the normal to the parabola y^2=4a x , both drawn at the same end of the latus rectum, and the axis of the parabola is 2sqrt(2)a^2 (b) 2a^2 4a^2 (d) none of these

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

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (1,-2+sqrt(2)) (d) none of these