Show that the circle on the chord `x cos alpha + y sin alpha - p=0` of the circle `x^2 + y^2 = a^2` as diameter is `x^2 + y^2 - a^2 - 2p (x cosalpha + y sinalpha-p)=0`.

Show that the circle on the chord xcosalpha+ ysinalpha-p = 0 of the circle x^2+ y^2 = a^2 as diameter is x^2 + y^2 - a^2 - 2p (xcosalpha + ysinalpha-p) = 0.

If the line x cosalpha + y sin alpha = P touches the curve 4x^3=27ay^2 , then P/a=

If the straight line represented by x cos alpha + y sin alpha = p intersect the circle x^2+y^2=a^2 at the points A and B , then show that the equation of the circle with AB as diameter is (x^2+y^2-a^2)-2p(xcos alpha+y sin alpha-p)=0

If the line y cos alpha = x sin alpha +a cos alpha be a tangent to the circle x^(2)+y^(2)=a^(2) , then

Find the value of p so that the straight line x cos alpha + y sin alpha - p may touch the circle x^(2) + y^(2)-2ax cos alpha - 2ay sin alpha = 0 .

The equation of the circle described on the common chord of the circles x^(2)+y^(2)+2x=0 and x^(2)+y^(2)+2y=0 as diameter, is

The equation of the circle on the common chord of the circles (x-a)^(2)+y^(2)=a^(2) and x^(2)+(y-b)^(2)=b^(2) as diameter, is

The equation of the circle described on the common chord of the circles x^2 +y^2- 4x +5=0 and x^2 + y^2 + 8y + 7 = 0 as a diameter, is

Show that the locus of P where the tangents drawn from P to the circle x^(2)+y^(2)=a^(2) include an angle alpha is x^(2)+y^(2)=a^(2)cosec^(2)(alpha)/2

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 is