The curve in the first quadrant for which the normal at any point `(x , y)` and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.

The length of normal at any point to the curve, y=c cosh(x/c) is

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

If eccentric angle of a point lying in the first quadrant on the ellipse x^2/a^2 + y^2/b^2 = 1 be theta and the line joining the centre to that point makes an angle phi with the x-axis, then theta - phi will be maximum when theta is equal to

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2 (b) x-y=2 2x-y=1 (d) none of these

If D is any point on the base B C produced, of an isosceles triangle A B C , prove that A D > A B .

With a given point and line as focus and directrix, a series of ellipses are described. The locus of the extremities of their minor axis is an ellipse (b) a parabola a hyperbola (d) none of these

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x^2+y^2=9 and the line joining their points of contact.