The normal PG to a curve meets the x-axis in G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.

The normal PG to a curve needs x axis in G if the distance of G from origin is twice the abscissa of p prove that the curve is rectangular hyperbola

The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a (1) ellipse (2) parabola (3) circle (4) hyperbola

The normal to a curve at P(x , y) meet the x-axis at Gdot If the distance of G from the origin is twice the abscissa of P , then the curve is a (a) parabola (b) circle (c) hyperbola (d) ellipse

Let the tangent at a point P on the ellipse meet the major axis at B and the ordinate from it meet the major axis at A. If Q is a point on the AP such that AQ=AB , prove that the locus of Q is a hyperbola. Find the asymptotes of this hyperbola.

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

The tangent at a point 'P' of a curve meets the axis of 'y' in N, the parallel through 'P' to the axis of 'y' meets the axis of X at M, O is the origin of the area of Delta MON is constant then the curve is (A) circle C) ellipse (D) hyperbola (B) parabola

The tangent at a point 'P' of a curve meets the axis of 'y' in N, the parallel through 'P' to the axis of 'y' meets the axis of X at M, O is the origin of the area of Delta MON is constant then the curve is (A) circle C) ellipse (D) hyperbola (B) parabola

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

The distance between the origin and the normal to the curve y=e^(2x)+x^(2) at x=0 is