tangent drawn to the ellipse `x^2/a^2+y^2/b^2=1` at point `'P'` meets the coordinate axes at points `A` and `B` respectively.Locus of mid-point of segment `AB` is

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

If the tangent drawn to the hyperbola 4y^2=x^2+1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid-point of AB is:

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

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.

Let P(theta_1) and Q(theta_2) are the extremities of any focal chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose eccentricity is e. Let theta be the angle between its asymptotes. Tangents are drawn to the hyperbola at some arbitrary points R. These tangent meet the coordinate axes at the points A and B respectively. The rectangle OABC (O being the origin) is completedm, then Q.Locus of point C is

Tangent at a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is drawn which cuts the coordinates axes at A and B the minimum area of the triangle OAB is ( O being origin )

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points whose eccentric angles are alpha-beta and alpha+beta The coordinates of their point of intersection are

Normal to the ellipse (x^2)/(64)+(y^2)/(49)=1 intersects the major and minor axes at Pa n dQ , respectively. Find the locus of the point dividing segment P Q in the ratio 2:1.

Consider the family ol circles x^2+y^2=r^2, 2 < r < 5 . If in the first quadrant, the common tangnet to a circle of this family and the ellipse 4x^2 +25y^2=100 meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB.