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`

A tangent to the ellipse x^2 / a^2 + y^2 / b^2 = 1 touches at the point P on it in the first quadrant & meets the coordinate axes in A & B respectively. If P divides AB in the ratio 3: 1 reckoning from the x-axis find the equation of the tangent.

The tangent drawn to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 , at point P in the first quadrant whose abscissa is 5, meets the lines 3x-4y=0 and 3x+4y=0 at Q and R respectively. If O is the origin, then the area of triangle OQR is (in square units)

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

Let the line y=mx and the ellipse 2x^(2)+y^(2)=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co - ordinate axes at (-(1)/(3sqrt2),0) and (0, beta) , then beta is equal to

Let the line y=mx and the ellipse 2x^(2)+y^(2)=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co - ordinate axes at (-(1)/(3sqrt2),0) and (0, beta) , then beta is equal to

Let F_1(x_1,0)" and "F_2(x_2,0) , for x_1 lt 0 " and" x_2 gt 0 , be the foci of the ellipse (x^2)/(9)+(y^2)/(8)=1 . Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of the area of the triangle MQR to area of the quadrilateral MF_1NF_2 is :

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

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 T×O Ndot