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[" origin to the points of intersection of the straight line "],[hx+ky=2hk" and the curve "(x-k)^(2)+(y-h)^(2)=c^(2)" are right "],[" angles,if "h^(2)+k^(2)=c^(2)" ."]

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Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

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

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

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

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

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

If the lines joining the origin to the points of intersection of the line y =mx +2 and the curve x^(2)+y^(2)=1 are right angles then

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))