Through the vertex `O` of the parabola `y^2=4a x` , two chords `O Pa n dO Q` are drawn and the circles on OP and OQ as diameters intersect at `Rdot` If `theta_1,theta_2` , and `varphi` are the angles made with the axis by the tangents at `P` and `Q` on the parabola and by `O R ,` then value of `cottheta_1+cottheta_2` is `-2tanvarphi` (b) `-2tan(pi-varphi)` 0 (d) `2cotvarphi`

Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q are drawn and the circles on OP and OQ as diameters intersect at Rdot If theta_1,theta_2 , and varphi are the angles made with the axis by the tangents at P and Q on the parabola and by O R , then value of cottheta_1+cottheta_2 is (a) -2tanvarphi (b) -2tan(pi-varphi) (c) 0 (d) 2cotvarphi

Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in

Through the vertex 'O' of parabola y^2=4x , chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ.

From an external point P , a pair of tangents is drawn to the parabola y^2=4xdot If theta_1a n dtheta_2 are the inclinations of these tangents with the x-axis such that theta_1+theta_2=pi/4 , then find the locus of Pdot

From an external point P , a pair of tangents is drawn to the parabola y^2=4xdot If theta_1a n dtheta_2 are the inclinations of these tangents with the x-axis such that theta_1+theta_2=pi/4 , then find the locus of Pdot

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 .

The tangents at the end points of any chord through (1, 0) to the parabola y^2 + 4x = 8 intersect

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

Through the vertex ' O^(prime) of the parabola y^2=4a x , variable chords O Pa n dO Q are drawn at right angles. If the variable chord P Q intersects the axis of x at R , then distance O R : (a)equals double the perpendicular distance of focus from the directrix. (b)equal the semi latus rectum of the parabola (c)equals latus rectum of the parabola (d)equals double the latus rectum of the parabola

Two tangents to the parabola y^2 = 4ax make angles theta_1,theta_2 with the x-axis. Then the locus of their point of intersection if cot theta_1 + cot theta_2=c is