For an ellipse `x^2/9+y^2/4=1` with vertices A and A', drawn at the point P in the first quadrant meets the y axis in Q and the chord A'P meets the y axis in M. If 'O' is the origin then `OQ^2-MQ^2`

Find the area of the region in the first quadrant enclosed by x-axis, line x = sqrt3y and the circle x^(2) + y^(2) = 4 .

If the tangent at the point P on the circle x^2+y^2+6 x+6 y=2 meets the straight line 5 x-2 y+6=0 at a point Q on the y -axis, then the length of P Q is

If the tangent at the point on the circle x^2+y^2+6x +6y=2 meets the straight ine 5x -2y+6 =0 at a point Q on the y- axis then the length of PQ is

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot

At a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 tangents PQ is drawn. If the point Q be at a distance (1)/(p) from the point P, where 'p' is distance of the tangent from the origin, then the locus of the point Q is

Find the equation of a line drawn perpendicular to the line x/4 + y/6 = 1 through the point , where it meets the y-axis.

P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.