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.

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)

Let A be the area of the region in the first quadrant bounded by the x-axis the line 2y = x and the ellipse (x^(2))/(9) + (y^(2))/(1) = 1 . Let A' be the area of the region in the first quadrant bounded by the y-axis the line y = kx and the ellipse . The value of 9k such that A and A' are equal is _____

The tangent to the ellipse (x^(2))/(25)+(y^(2))/(16)=1 at point P lying in the first quadrant meets x - axis at Q and y - axis at R. If the length QR is minimum, then the equation of this tangent is

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

Let F_1(x_1,0) and F_2(x_2,0), for x_1 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 area of the triangle MQR to area of the quadrilateral MF_1 NF_2 is