If `P(t^(2),2t),tin[0,2]`, is an arbitrary point on the parabola `y^(2)=4x`, Q is the foot of perpendicular from focus S on the tangent at P, then the maximum area of `DeltaPQS` is

If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x ,Q is the foot of perpendicular from focus S on the tangent at P , then the maximum area of P Q S is (a) 1 (b) 2 (c) 5/(16) (d) 5

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

Let P be a point on the parabola y^(2) = 4ax with focus F . Let Q denote the foot of the perpendicular from P onto the directrix . Then (tan anglePQF)/(tananglePFQ) is_

If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpendicular drawn from the point P on the directrix of the parabola, then find length of each sides of an equilateral triangle SMP(where S is the focus of the parabola).

Find the foot of perpendicular drawn from the point (2, 2) to the line 3x - 4y + 5 = 0

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

P is a point on the straight line 7x-4y-29=0 . If the foot of the perpendicular drawn from P on the line 5x+2y+18=0 be N(-2,-4) , find the coordinates of P.

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .