find the value of p so that 3x + 4y - p =0 is a tangent to the circle ` x^(2) + y^(2) - 64 =0`

If 3x+4y+k=0 is a tangent to the circle x^(2)+y^2=16" then k"=

The straight line 3x-4y +7 = 0 is a tangent to the circle x^(2) + y^(2) + 4x + 2y + 4 = 0 at P, find the equation of its normal at the same point.

If 3x - 4y + k = 0 is a tangent to x^(2) - 4y^(2) = 5 find the value of k.

The tangent from the point of intersection of the lines 2x – 3y + 1 = 0 and 3x – 2y –1 = 0 to the circle x^(2) + y^(2) + 2x – 4y = 0 is

If the line 3x-2y+p = 0 is normal to the circle x^(2)+ y^(2) = 2x-4y ,then p will be

Find the value of p so that the three lines 3x + y - 2 = 0 , p x + 2 y - 3 = 0 and 2x -y -3 = 0 may intersect at one point.

Find the equation of the tangent to the circle x^(2) + y^(2) - 2x + 8y - 23 = 0 at the point P(3, - 10) on it.

If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles x^(2)+y^(2)+2x-4y-20=0 and x^(2)+y^(2)-4x+2y-44=0 is 2:3, then the locus of P is a circle with centre .