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 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 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

In the curve y=c e^(x/a) , the sub-tangent is constant sub-normal varies as the square of the ordinate tangent at (x_1,y_1) on the curve intersects the x-axis at a distance of (x_1-a) from the origin equation of the normal at the point where the curve cuts y-a xi s is c y+a x=c^2

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.

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.

Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1,2).

Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent art a point is twice the abscissa and which passes through the point (1,2).

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