Tangent are drawn from two points `(x_1, y_1) and (x_2, y_2)` to `xy = c^2`. The conic passing through the two points and through the four points of contact will be circle if (A) `x_1 x_2 = y_1 y_2` (B) `x_1 y_2 = x_2 y_1` (C) `x_1 y_2 + x_2 y_1 = 4c^2` (D) `x_1 x_1 + y_1 y_2 = 4c^2`

From the point (x_1, y_1) and (x_2, y_2) , tangents are drawn to the rectangular hyperbola xy=c^(2) . If the conic passing through the two given points and the four points of contact is a circle, then show that x_1x_2=y_1y_2 and x_1y_2+x_2y_1=4c^(2) .

Tangents are drawn from the points (x_(1), y_(1))" and " (x_(2), y_(2)) to the rectanguler hyperbola xy = c^(2) . The normals at the points of contact meet at the point (h, k) . Prove that h [1/x_(1) + 1/x_(2)] = k [1/y_(1)+ 1/y_(2)] .

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x + y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x - y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

If the line joining the points (_x_1, y_1) and (x_2, y_2) subtends a right angle at the point (1,1), then x_1 + x_2 + y_2 + y_2 is equal to

Write the condition of collinearity of points (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a) x_1, a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2),x_1/x_2 are in GP (d) x_1x_2+y_1y_2=a^2

The ratio in which the line segment joining P(x_1,\ y_1) and Q(x_2,\ y_2) is divided by x-axis is (a) y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

If A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the median through A . Show that : |(x, y, 1), (x_1, y_1, 1), (x_2, y_2, 1)| + |(x, y, 1), (x_1, y_1, 1), (x_3, y_3, 1)|=0