Two lines are drawn from point `P(alpha, beta)` which touches `y^2 = 8x` at A,B and touches `x^2/4 + y^2/6 = 1` at C,D, then-

Tangents are drawn from point P on the curve x^(2) - 4y^(2) = 4 to the curve x^(2) + 4y^(2) = 4 touching it in the points Q and R . Prove that the mid -point of QR lies on x^(2)/4 - y^(2) = (x^(2)/4 + y^(2))^(2)

The line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point

If line T_1 touches the curve 8y=(x-2)^2 at (-6,8) and line T_2 touches the curve y=x+3/x at (1,4), then

If line x cos alpha + y sin alpha = p " touches circle " x^(2) + y^(2) =2ax then p =

Tangents drawn from the point P(1,8) to the circle x^(2) + y^(2) - 6x - 4y -11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is:

The line x sin alpha - y cos alpha =a touches the circle x ^(2) +y ^(2) =a ^(2), then,

If the length of the tangent drawn from (alpha,beta) to the circle x^(2)+y^(2)=6 be twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0, then prove that alpha^(2)+beta^(2)+4 alpha+4 beta+2=0