show that the area of the triangle inscribed in the circle `x^(2)/a^(2)+y^(2)/b^(2)=1` meet the ellipse respictively at P,Q,R so that P,Q,R lie on the same side of the major axis as A,B,C respictively. Prove that the normal to the ellipse drawn at the points P,Q and R are concurrent.

Let ABC be an equilateral triangle inscribed in the circle x^2+y^2=a^2 . Suppose pendiculars from A, B, C to the ellipse x^2/a^2+y^2/b^2=1,(a > b) meets the ellipse respectivelily at P, Q, R so that P, Q , R lies on same side of major axis as A, B, C respectively. Prove that the normals to the ellipse drawn at the points P Q nad R are concurrent.

P and Q are corresponding points on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the auxiliary circle respectively . The normal at P to the elliopse meets CQ at R. where C is the centre of the ellipse Prove that CR = a +b

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

The tangent and normal to the ellipse x^2+4y^2=4 at a point P(theta) on it meets the major axis in Q and R respectively. If 0 < theta < pi/2 and QR=2 then show that theta=

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

If normal at any poin P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.

A normal inclined at 45^@ to the axis of the ellipse x^2 /a^2 + y^2 / b^2 = 1 is drawn. It meets the x-axis & the y-axis in P & Q respectively. If C is the centre of the ellipse, show that the area of triangle CPQ is (a^2 - b^2)^2/(2(a^2 +b^2)) sq units

The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on the line y = c. Prove that the sides of the triangle PQR touch the parabola x^2 = 2cy.