Find the value of p so that `x^2 + y^2 + 8x + 10 y + p = 0` is the equation of a circle of radius 7 units.

The radius of the circle : x^2 + y^2-8x + 10y- 12 =0 is:

Find the centre and radius of the circle : x^2 + y^2+ 8x + 10y- 8 =0 .

Find the centre and radius of the circle : x^2 + y^2- 8x+ 10y- 12 = 0 .

Find the value of P such that the vertex of y=x^2+2p x+13 is 4 units above the x-axis.

If y = 2x is a chord of a circle x^2+ y^2-10x = 0 , find the equation of the circle with this chord as diameter.

The intercept on line y = x by circle x^2 + y^2- 2x = 0 is AB. Find equation of circle with AB as a diameter.

Find the greatest value of x^3y^4 if 2x + 3y = 7 and x>=0,y>=0 .

Find the equation of the image of the circle : x^2 + y^2 + 8x-16y + 64=0 in the mirror x = 0.

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

Find the values of theta and p, if the equation x cos theta + y sin theta = p is the normal form of the line sqrt3 x+y + 2 = 0 .