From a point P perpendicular tangents PQ and PR are drawn to ellipse `x^(2)+4y^(2) =4`, then locus of circumcentre of triangle PQR is

Tangents PA and PB are drawn to the circle x^(2)+y^(2)=4, then locus of the point P if PAB is an equilateral triangle,is equal to

From point P(8,27) tangents PQ and PR are drawn to the ellipse (x^(2))/(4)+(y^(2))/(9)=1. Then, angle subtended by QR at origin is

From a variable point P a pair of tangent are drawn to the ellipse x^(2)+4y^(2)=4, the points of contact being Q and R. Let the sum of the ordinate of the points Q and R be unity.If the locus of the point P has the equation x^(2)+y^(2)=ky then find k

If from a point P, tangents PQ and PR are drawn to the ellipse (x^(2))/(2)+y^(2)=1 so that the equation of QR is x+3y=1, then find the coordinates of P.

From the point P(16,7), tangents PQ and PR are drawn to the circle x^(2)+y^(2)-2x-4y-20=0 If C is the centre of the circle,then area of quadrilateral PQCR is

From a point P, tangents PQ and PR are drawn to the parabola y^(2)=4ax . Prove that centroid lies inside the parabola.

From a point P, tangents PQ and PR are drawn to the parabola y ^(2)=4ax. Prove that centrold lies inside the parabola.

From a point P=(3,4) perpendiculars PQ and PR are drawn to line 3x+4y-7=0 and a variable line y-1=m(x-7) respectively then maximum area of triangle PQR is :