If the line`y-sqrt(3)x + 3=0` cuts the parabola `y^2=x + 2` at A and B, then find the value of PA.PB(where `P=(sqrt(3),0)`

If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to

If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0 at A and B , then the maximum of PA+PB is

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then the tangent of the angle subtended by line segment A B at the origin is (8sqrt(3))/(205) (b) (8sqrt(3))/(209) (8sqrt(3))/(215) (d) none of these

If the lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.

If the vertex of the parabola is (3,2) and directrix is 3x+4y-(19)/7=0 , then find the focus of the parabola.

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot