Find the equation to the pair of straight lines joining the origin to the intersections oi the straight line `y=mx + c` and the curve `x^2 + y^2=a^2` . Prove that they are at right angles if `2c^2=a^2(1+m^2)`.

Prove that The lines joining the origin to the points of intersection of the line 3x-2y =1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are are at right angles.

If the lines joining the origin to the intersection of the line y=nx+2 and the curve x^2+y^2=1 are at right angles, then the value of n^2 is

Prove that the straight lines joining the origin to the point of intersection of the straight line h x+k y=2h k and the curve (x-k)^2+(y-h)^2=c^2 are perpendicular to each other if h^2+k^2=c^2dot

Find the equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=0 and x^2+y^2-2x-4y=4 .

Find the equation of the straight line passing through the point (2,1) and through the point of intersection of the lines x+2y = 3 and 2x-3y=4

The lines joining the origin to the points of intersection of 2x^2 + 3xy -4x +1 = 0 and 3x + y=.1 given by

If the straight lines joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2 +x-2y -m =0 are perpendicular to each other , then the value of m should be

Find the equation to the pair of straight lines joining the origin to the intersections oi the straight line `y=mx + c` and the curve `x^2 + y^2=a^2` . Prove that they are at right angles if `2c^2=a^2(1+m^2)`.

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