prove that for a suitable point `P` on the axis of the parabola, chord `A B` through the point `P` can be drawn such that `[(1/(A P^2))+(1/(B P^2))]` is same for all positions of the chord.

How many chords can be drawn through 20 points on a circle ?

How many chords can be drawn through 21 points on a circle?

The point of intersection of the tangents of the parabola y^(2)=4x drawn at the end point of the chord x+y=2 lies on

From a point P outside a circle with centre at C, tangents PA and PB are drawn such that 1/(CA)^2+ 1/(PA)^2=1/16 , then the length of chord AB is

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

If the two tangents drawn from a point P to the parabola y^(2) = 4x are at right angles then the locus of P is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

The equation of chord AB of the circle x^2+y^2=r^2 passing through the point P(1,1) such that (PB)/(PA)=(sqrt2+r)/(sqrt2-r) , (0ltrltsqrt(2))