The line `3x+6y=k` intersects the curve `2x^2+3y^2=1` at points `Aa n dB` . The circle on `A B` as diameter passes through the origin. Then the value of `k^2` is__________

For the curve y = 4x^(3) – 2x^(5) , find all the points at which the tangent passes through the origin.

The point of intersection of the curves y^(2) = 4x and the line y = x is

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

A line L passing through the point (2, 1) intersects the curve 4x^2+y^2-x+4y-2=0 at the point Aa n dB . If the lines joining the origin and the points A ,B are such that the coordinate axes are the bisectors between them, then find the equation of line Ldot

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through

If the lines x+y=6a n dx+2y=4 are diameters of the circle which passes through the point (2, 6), then find its equation.

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

The line y=(3x)/4 meets the lines x-y=0 and 2x-y=0 at points Aa n dB , respectively. If P on the line y=(3x)/4 satisfies the condition P AdotP B=25 , then the number of possible coordinates of P is____

The tangents to the curve y = (x - 2)^(2) - 1 at its points of intersectio with the line x - y = 3, intersect at the point

The graph y=2x^3-4x+2a n dy=x^3+2x-1 intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.